Theoretically,stars formed from the collapse of cores in molecular clouds.Historically,the core had been assumed to be a singular isothermal sphere(SIS),andthe collapse had been investigated in a self-similar manner.When the rotation andmagnetic fields lead to non-symmetric collapse,a spheroidal shape may occur.Here,the result of the centrifugal force and magnetic field gradient is assumed to be inthe normal direction to the rotational axis,and its components are supposed to bea fractionβof the local gravitational force.In this research,a collapsing SIS coreis considered to find the importance that the parameterβplays in the oblateness ofthe mass shells,which are the crests of the expansion waves.We apply the Adomiandecomposition method to solve the system of nonlinear partial differential equationsbecause the collapse does not occur in a spherically symmetric and self-similar manner.In this way,we obtain a semi-analytical relation for the mass infall rate M ofthe shells in the envelope.Near the rotational axis,M decreases with the increase ofthe non-dimensional radiusξ,while a direct relation is observed between M/andξin the equatorial regions.Also,the values of M in the polar regions are greater than theirequatorial values,and this difference occurs more often at smaller values ofξ.Overall,the results show that before reaching the crest of the expansion wave,the visible shapeof the molecular cloud cores can evolve into oblate spheroids.The ratio of major tominor axes of oblate cores increases when increasing the parameter β,and its valuecan approach the observed elongated shapes of cores in the maps of molecular clouds,such as those in Taurus and Perseus.