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In this paper, we studied the 2D steady laminar boundary layer flow and heat transfer of Casson based nanofluid over an exponentially vertical stretching and shrinking sheet using one phase model. The thermal radiation and heat source/sink parameters are incorporated in the heat transfer equation and the slip parameters for the velocity and temperature are considered in the boundary conditions. The similarity variables have been used to convert the governing equations as a system of partial differential equations to the ordinary differential equations. The transformed equations are then solved by applying shooting technique, shootlib in Maple software. The numerical solutions for the governing equations indicate that the triple solutions arise when high suction is imposed for both stretching/shrinking sheet at certain ranges of the pertinent parameters. To examine the stability of the solutions, stability analyses is done by using BVP4c in Matlab software. The first solution is found to be a stable solution and physical realizable while the remaining solutions are not stable. The inclusion of three different nanoparticles shows that Copper – Casson nanofluid has the highest heat transfer rate compared to Aluminum-Casson and Graphite Oxide-Casson nanofluid.