Dissertation (MSc Mathematics)We find new exact solutions to Einstein-Maxwell field equation for neutral anisotropy stellar stars with Van der Waals equation of state. We adopted Sunzu, Maharaj and Ray‘s metric function and measure of anisotropy. The solutions are obtained after considering the transformed Einstein-Maxwell field equations for neutral anisotropic matter. In our models, we regain previous anisotropic and isotropic results as a special case. We consider the space-time geometry to be static spherically symmetry. The exact solutions to the Einstein-Maxwell field equations corresponding to our models are found explicitly in terms of elementary functions namely simple algebraic functions. The gravitational potentials and matter variables generated are well behaved. We also generate relativistic stellar masses consistent with the stars PSR J1614-2230, Vela X-1, 4U 1538-52, LMC X-4, SMC X-4, Cen X-3, Her X-1, SAX J1808.4-3658 and EXO 1785-248.