A theoretical study of the problem of stagnation point flow, heat and mass transfer in a Maxwell fluid over a surface with variable wall heat and mass flux in the presence of heat generation/absorbtion is investigated. This work is extended from the previous published study of Sadeghy et al. [16]. The boundary layer equations describing the problem are transformed to a system of non-linear ordinary differential equations. The resulting system of non-linear ordinary differential equations is solved numerically using Chebyshev spectral method. The results show that the Deborah number has the effect of reducing the temperature and the concentration inside the boundary layer and enhancing the velocity.