A new approach is presented for calculating Hantush's M function which arises often in analytical solutions for groundwater pumping models. We develop an algorithm of implementing Hantush's M function calculations, in which binomial expansion theorem is employed. This algorithm is advantageous in the accurate calculation of Hantush's M function. The formulae by which Hantush's M function is expressed are uniform, and their application to the calculation of dynamics of groundwater mounding beneath recharge zones presents no difficulties using a computer. Finally, simple results are presented and discussed.