Variational Monte Carlo (VMC) methods are extensively used for problems in molecular, condensed matter and nuclear physhcs. Quantum Monte Carlo methods offer an effective way to deal with many body problems in nuclear physics. The nuclear Hamiltonian has a compicated operator form with several terms. The variational wave function suggested on physical grounds also has a complex correlation structure. In this work nuclei with mass no. A = 3 to 6 ate treated under VMC framework. Several improvements in the variational wave function are suggested and VMC calculations are performed using potentials that include the Argonne V-18 and the three body Urbana -IX. Space exchange effects present in lambda hypernuclei are also briefly looked into. The nuclear hamiltonian, the variational wave function and the Monte Carlo technique is described in detail.