The service life of concrete structures depend largely on the durability of concrete. The durability of concrete is influenced by mass transport mechanisms that can have severe deteriorating effects. Transport of water in concrete is of paramount importance as water can act as a carrier of ions such as chlorides which can corrode the reinforcement and reduce the service life of concrete structures. The main objective of this thesis is to study moisture transport through capillary absorption in concrete. Numerical simulation of moisture transport is performed through lattice elements with an irregular mesh configuration. New computational tools are developed and compared with the existing tools in terms of effectiveness to simulate moisture transport in homogeneous uncracked concrete. The existing numerical model uses approximate volume of transport elements to determine the volumetric capacity of elements. During discretization of the governing equation, the variation of diffusivity of the elements is approximated as a uniform mean distribution and an explicit time stepping scheme is implemented which has consequences on the flow equilibrium at each time step. In the proposed numerical model, exact volume of transport elements is considered and during the discretization of governing equations, exponential variation of diffusivity is considered along with an implicit time stepping scheme. Moisture transport is accurately simulated in uncracked homogeneous concrete even by using the existing model as validated through experimental results. Both the models are compared through error analysis by varying mesh size and time step. Moisture flow through different diffusivity coefficients is simulated using both the models and it is observed that the existing model suffers from oscillations in the saturation level during initial stages of flow due to inability of the existing model to maintain flow equilibrium at each time step. The proposed model on the other hand shows no such oscillations due to the flow equilibrium being maintained at each time step. Mesh size, magnitude of time step and diffusivity coefficient are shown to be the parameters limiting the effectiveness of either of the models. A single discrete crack is considered within the domain and its influence on moisture transport is observed. The nature of the crack is considered through two approaches. In the first approach, crack is considered as an additional porous phase in cement matrix and the entire volume occupied by the crack is considered to be a void. In the second approach, in addition to considering the porous nature of crack, moisture surface interaction between the water surface and crack walls is also considered. Horizontal moisture distribution around a planar crack is simulated using both the approaches which show similar results as in the experiment. The vertical moisture distribution is simulated within a wedge shaped crack and the results are compared with experimental observations. The first approach shows a slower rate of saturation of the crack as compared to the experiment. The second approach shows the vertical saturation of the crack similar to the experiment. A comparison between the Delaunay and Voronoi modelling techniques of moisture simulation in cracked domain is discussed. It is shown that the presence of a crack accelerates the moisture transport in concrete as it exposes additional surface of concrete from where water can penetrate in the material and also increases the diffusivity of the concrete material lying in the vicinity of the crack. Moisture transport is simulated in concrete considering its multi-phase nature. Concrete is considered to be composed of three phases i.e. cement paste, aggregates and ITZ around aggregates. Aggregates are considered to be impervious which do not allow the flow of moisture through them which slows down the flow in concrete. The ITZ around the aggregates have higher transport properties and accelerate the flow. A numerical framework is formulated in which spherical aggregates are projected on lattice elements which are assigned transport properties pertaining to the phase of concrete they represent. Moisture transport is simulated and compared with experimental results where an increase of volume fraction of aggregates leads to a decrease of cumulative saturation level. The influence of ITZ is observed on a local and global scale by varying the ITZ diffusivity coefficient. The moisture simulation is also modelled on a finer mesh to see the effect of mesh refinement. Finally, moisture transport is simulated in a numerical model that combines a planar crack along with heterogeneities and flow is observed at different time stages.