The mass transfer of ozone and oxygen into water through non-porous membranes was studied using computational fluid dynamics (CFD) modelling and fundamental convection-diffusion theory. Ozone is a gaseous oxidant that is widely applied in drinking water treatment. Membrane contactors are an alternative to conventional gas dispersion methods for injection of ozone gas mixtures into water. Few studies have explored computational approaches for membrane based ozone transport. In this investigation, quantitative concentration profiles across a single polydimethylsiloxane (PDMS) capillary membrane tube with internal gas flow and external liquid flow were obtained, including single mass transfer resistances and overall mass transfer coefficients for ozone and oxygen for varying membrane lengths, thicknesses, and laminar flow liquid side velocities. Both the influence of diffusivity and solubility of gases in the membrane were considered with the applied model. Previous studies have neglected the solubility of gases in the membranes in their analysis of ozone and oxygen gas fluxes. This work shows that the solubility has a significant impact of the overall mass transfer coefficients, in particular for oxygen. The main resistance for ozone was found in the liquid side, while for oxygen it was in the membrane. Mass transfer correlations based on heat transfer analogies revealed Sherwood (Sh) correlations for ozone and oxygen with good agreement to literature data, indicating that the applied computational model returns sensible results. The outcome of this study provides an initial basis for computational predictions of ozone and oxygen mass transfer for different membrane materials, flow conditions and reactor designs.