Numerical methods including homotopy perturbation method and homotopy variational method are applied to solve moving boundary and isoperimetric problems. homotopy perturbation method does not depend upon a small parameter in the equation, homotopy is constructed with an imbedding parameter p, which is considered as a "small parameter". Finally, we use combined homotopy perturbation method and Green's function method for solving second order problems. In variational method, general Lagrange multiplier is introduced to construct correction functional for the variational problems. Some examples are given to illustrate the effectiveness of methods. The results show that these methods provides a powerful mathematical tools for solving problems.