<p>The nonlinear dispersive modified Benjamin-Bona-Mahony (NDMBBM) equation, which is one of the important nonlinear evolution equations, emerges as a mathematical model for surface long waves in nonlinear dispersive media. This equation is widely used in physics and mathematics to explain many real-world phenomena. The analytic solutions for the NDMBBM are found by utilizing a direct method with help of the Jacobi elliptic functions in this study. To get the elementary and elliptic solutions of this equation, the solutions of an auxiliary ordinary differential equation (ODE) are used. Various analytical solutions of the NDMBBM equation are obtained in terms of the rational, trigonometric, hyperbolic, and complex functions. The solitary wave solutions and the different types of soliton solutions are also attained by the presented method. The most extensive set of solutions of the NDMBBM equation in the literature are found and given by tables. Besides, to demonstrate the effectiveness and reliability of the method, four examples are presented and some of the found solutions are illustrated with 2D and 3D graphs as evidence of visualization. Moreover, these solutions are useful for further development of the relevant model in future studies. Furthermore, proposed method is simple, reliable, and effective for solving numerous different partial differential equations (PDEs).</p>