Scaffolds for tissue engineering are usually designed to support cell viability with large adhesion surfaces and high permeability to nutrients and oxygen. Recent experiments support the idea that, in addition to surface roughness, elasticity and chemistry, the macroscopic geometry of the substrate also contributes to control the kinetics of tissue deposition. In this study, a previously proposed model for the behavior of osteoblasts on curved surfaces is used to predict the growth of bone matrix tissue in pores of different shapes. These predictions are compared to in vitro experiments with MC3T3-E1 pre-osteoblast cells cultivated in two-millimeter thick hydroxyapatite plates containing prismatic pores with square- or cross-shaped sections. The amount and shape of the tissue formed in the pores measured by phase contrast microscopy confirms the predictions of the model. In cross-shaped pores, the initial overall tissue deposition is twice as fast as in square-shaped pores. These results suggest that the optimization of pore shapes may improve the speed of ingrowth of bone tissue into porous scaffolds.