<p>The (3+1)-dimensional telegraphic equation is widely studied in the field of physical sciences and engineering. This study derives analytical and numerical solutions for this model using Lie symmetry analysis and the finite element method. Initially, we establish the invariant condition in light of the Lie symmetry method concerning the telegraphic equation. Subsequently, Lie symmetries are acquired with the aid of this invariant condition. These Lie symmetries are further employed to acquire the vector fields. Moreover, as an outcome of these vector fields, the optimal system of subalgebras is produced. Further, under each subalgebra, we obtained the reduced equation for the similarity solution and similarity variables. In conclusion of the study, these reduced equations are solved for exact solutions. Moreover, for the simulation of a reduced equation using the finite element method, we choose the initial data and BCs from the exact solution of these reduced equations. After that, using the back transformation, i.e. similarity solutions and similarity variables, exact solutions of the main telegraphic equation are established. The solutions obtained are in the shape of trigonometric, exponential, and hyperbolic functions.</p>