ABSTRACT This research aims to study the mapping method and apply it on some nonlinear partial differential equations. From our study of the mapping method we inferred four well-know methods classified under the symbolic computational methods, using specific values for the coefficients of the mapping method, one of these methods is the hyperbolic function method which has been applied on the nonlinear family of third order Korteweg-de Vries equations. Finally we applied the mapping method to the general Pade′II equation and the (2+ 1)-dimensional Konopelchenko-Dubrovsky equation. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions, trigonometric functions, rational functions and elliptic functions.