In this paper, a computational method called the AGM technique is applied to solve the governing equations of a physical problem. This problem is related to the analysis of the motion of a spherical particle under the influences of a fluid flow. After solving the nonlinear equations using the Akbari–Ganji Method (AGM), the precision of outcomes is evaluated by comparing them with the numerical technique. The AGM demonstrates approximations with high accuracy to obtain the analytical solutions to the present problem. The results show that the velocity profiles have different trends with the increase of time, so the radial velocity decreases with time, still, the angular velocity increases with the increase of time.