The objective of this work is to use Optimal Homotopy Asymptotic Method (OHAM), a new semi-analytic approximating technique, for solving linear and nonlinear initial and boundary value problems. The semi analytic solutions of nonlinear fourth order, eighth order, special fourth order and special sixth order boundary-value problems are computed using OHAM. Successful application of OHAM for squeezing flow is a major task in this study. This work also investigates the effectiveness of OHAM formulation for Partial Differential Equations (Wave Equation and Korteweg de Vries). OHAM is independent of the free parameter and there is no need of the initial guess as there is in Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM). OHAM works very well with large domains and provides better accuracy at lower-order of approximations. Moreover, the convergence domain can be easily adjusted. The results are compared with other methods like HPM, VIM and HAM, which reveal that OHAM is effective, simpler, easier and explicit.