This study investigates the size effect on the compressive strength of foamed concrete at the mesoscale level combining X-ray computed tomography (X-CT) and a discrete lattice model. Image segmentation techniques and X-CT were employed to obtain virtual specimens comprising hydrated cement paste and air voids. The lineal-path function and pore size distribution was used to characterise the air void structure. A two-dimensional lattice fracture model of foamed concrete considering different wet densities was established. The model was verified experimentally at a wet density of 700 kg/m³ and then used to predict the strengths of specimens with wet densities of 600 and 800 kg/m³. Square and rectangular specimens (slenderness ratio = 2) with widths of 10, 20, 40, 70.7, and 100 mm were investigated. Results show that the air void structure significantly influences the observed size effect on the compressive strength in the investigated size range. A random forest regressor was used to predict the compressive strength of the foamed concrete; the regressor yielded satisfactory results. Finally, existing analytical size effect models were used to fit the simulated strength. Although good fitting was achieved, special attention should be given to the applicable range and physical meaning of fitted empirical parameters.