Nonlinear hydromagnetic two dimensional steady, laminar, boundary layer flow of a viscous, incompressible, electrically conducting and radiating fluid with variable conductivity and nonlinear Rosseland approximation thermal radiation past a nonlinearly stretching porous surface is analysed in the presence of a variable magnetic field. The fluid is assumed to be a gray, emitting, absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. Fourth-Order Runge-Kutta shooting method along with the Nachtsheim-Swigert iteration for satisfaction of asymptotic boundary conditions is utilized for obtaining the numerical solution of the resulting nonlinear differential equations. The numerical results for velocity and temperature distribution are obtained for different values of velocity exponent parameter, magnetic interaction parameter, porosity parameter, radiation parameter, surface temperature parameter, variable thermal parameter and Prandtl number and are shown graphically. Numerical values of Skin friction coefficient and dimensionless and rate of heat transfer are also obtained and tabulated. © Research India Publications.