Results from a numerical investigation of one-dimensional, laminar flame quenching with constant and time-dependent pressure variations are reported herein. A description of flame quenching and post-flame oxidation processes for the global reaction A + B → C is obtained from a solution of a simplified form of the non-linear conservation of mass, momentum and energy equations in a planar flow field. These equations were reduced to finite difference form and the time-dependent pressure was input via either an integrated form of the energy equation or a third-order polynomial law. Numerical calculations were performed at constant pressure, combustion bombtype conditions and under rapid decompression during quenching. One-dimensional head-on quenching distances, hydrocarbon concentration levels and gas properties were obtained for a variety of stoichiometric values in a propane/airtype mixture. Results presented indicate that the quenching distance is primarily controlled by the thermal conduction process; however, residual hydrocarbon levels are intimately related to post-quenching diffusion, oxidation kinetics and the during which they occur.