In this paper, we discuss similarity reductions for problems of radiative and magnetic field effects on free-convection and mass-transfer flow past a semi-infinite vertical flat plate. Two cases are considered: Lie group analysis applied to uniform magnetic fields, and Scaling transformations applied to non-uniform magnetic fields. In particular, we determine new similarity reductions and find an analytical solution for the uniform magnetic field, by using Lie group method. Numerical results are presented and discussed for various values of the parameters governing the problem