This article studies the unsteady MHD free flow of a Casson fluid past an oscillating vertical plate with constant wall temperature. The fluid is electrically conducting and passing through a porous medium. This phenomenon is modelled in the form of partial differential equations with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The corresponding non-dimensional equations with conditions are solved using the Laplace transform technique. Exact solutions for velocity and energy are obtained. They are expressed in simple forms in terms of exponential and complementary error functions of Gauss. It is found that they satisfy governing equations and corresponding conditions, and are reduced to similar solutions for Newtonian fluids as a special case. Expressions for skin-friction and Nusselt number are also evaluated. Computations are carried out and the results are analysed for emerging flow parameters.