This paper focuses on deriving new approximate analytical solutions in wedge-shaped aquifers. The proposed methodology is applicable to any type of aquifer namely, leaky, confined and unconfined, under both steady state and transient flow conditions. By applying the method of images and seperating the flow field into sections using physical arguements, analytical expressions are obtained for the drawdown function. In contrast to the conventional theory, the proposed solutions are applicable to arbitrary wedge angle. Comparison of the results of the derived approximate analytical solutions to numerical ones, is considered necessary to ensure its validity. MODFLOW, a well-known numerical tool is used to calculate the numerical results. The results indicate that the boundary conditions are fully observed, the drawdown is feasible to be calculated at any point of the real flow field (continuity of the drawdown function) and discrepancies compared to numerical results are considered negligible. The main advantage of the proposed procedure is that it can be easily used in conjunction with meta-heuristic algorithms to solve groundwater resources optimization problems.