The effect of the mass transpiration parameter on the viscous gas flow past a porous stretching/shrinking sheet in the presence of Navier's slip is investigated, and also, the mass transfer characteristics are examined. The physical flow problem executes the Navier–Stokes and the mass equation, which forms the system of nonlinear partial differential equations. These are transformed via similarity variables into a system of ordinary differential equations. The slip flow model of the total mass transfer on the moving sheet is modeled by introducing gas slip velocity. The total mass transfer on the moving sheet is modeled by inducing slip models of first and second order. Further, the suction which induces the slip velocity as opposed to the surface movement is examined. The mass suction‐induced slip forces the adjacent gases to flow in the reverse direction to sheet movement. Thus, the solution space expands with the slip‐induced suction and sheet movement. In the mass injection case, the induced slip increases the effect of the fluid flow for sheet movement. Upon all previous flow models, the present investigation is significant due as it investigates the mass transfer of viscous gasses flow past a porous medium in the presence of slip and mass transpiration.