The convective Casson fluid flow past a Riga plate is investigated theoretically. The flow properties are elucidated through the analytical solutions of transport equations which are acquired by adopting the Laplace transform technique. This study mainly focuses on nonlinear flow characteristics under radiation, permeability and the wall parallel Lorentz force. The positive modified Hartmann number refers to the aiding flow which enhances the flow speed. The comparison between Newtonian and non-Newtonian fluid flow subject to the wall parallel Lorentz force has also been done graphically. Further, the results of this Casson fluid flow model correlated with the vertical flow under buoyancy effect.