Tissue engineering scaffolds are designed to support tissue self-healing within physiological environments by promoting the attachment, growth and differentiation of relevant cells. Newly formed tissue must be supplied with sufficient levels of oxygen to prevent necrosis. Oxygen diffusion is the major transport mechanism before vascularization is completed and oxygen is predominantly supplied via blood vessels. The present study compares different designs for scaffolds in the context of their oxygen diffusion ability. In all cases, oxygen diffusion is confined to the scaffold pores that are assumed to be completely occupied by newly formed tissue. The solid phase of the scaffolds acts as diffusion barrier that locally inhibits oxygen diffusion, i.e. no oxygen passes through the scaffold material. As a result, the oxygen diffusivity is determined by the scaffold porosity and pore architecture. Lattice Monte Carlo simulations are performed to compare the normalized oxygen diffusivities in scaffolds obtained by the foam replication (FR) method, robocasting and sol–gel foaming. Scaffolds made by the FR method were found to have the highest oxygen diffusivity due to their high porosity and interconnected pores. These structures enable the best oxygen supply for newly formed tissue among the scaffold types considered according to the present numerical predictions.