A process for the selective oxidation of olefins to epoxides comprising the step of contacting the olefin (propylene or ethylene) with an oxidant (hydrogen peroxide) in the presence of a Lewis acid oxidation catalyst (MTO), organic base (pyridine or its N-oxide), in a solvent system comprising an organic water-miscible solvent (methanol). The system is pressurized using either the olefin itself or by adding an inert pressurizing gas (nitrogen) to increase the pressure between 230 and 700 psi at a temperature between 0.7 and 1.3 times the critical temperature of the olefin. The resulting increased solubility of the olefin in the organic solvent system increases the selectivity and yield of the desired epoxide (propylene oxide or ethylene oxide).