Theoretical well function formulations in confined aquifer, leaky or unconfined aquifer types were originally developed to analyze the transient response of the ideal aquifer settings (i.e., homogeneous, isotropic medium, constant withdrawal rate, negligible well-bore storage and skin effects, etc.). Any deviations from the idealization of the aquifer settings inversely affect the estimation performance, which may result in an unrealistic interpretation of pump test analysis. A radial basis function collocation method (RBFCM)-based estimation procedure was proposed to elaborate the aquifer parameters in homogeneous and heterogeneous porous medium in the present work. The potential drawbacks of the classical curve matching techniques and the derivative-based estimation methods have been evaded without dense computation efforts using RBFCM. The proposed method as a default application procedure requires no additional parameter, no initial guess, no interpolation or any complicated derivative calculation to assess the aquifer parameters. The suggested approach, therefore, provides a greater degree of flexibility in the estimation and the same level of accuracy when compared to the existing methods used in hydrology practice. This study also reveals the use of proposed method as a diagnostic tool to identify aquifer character by tracking the aquifer parameter variation in time as well as the potential use of RBFCM as an inverse solution technique in the hydrogeology problems.