The aim of this paper is to study a nonlinear hyperbolic free boundary value problem. The technique of a non-iterative transformation to the numerical solution of a free boundary value problem is employed. (The hyperbolic model describes the time dependent velocity impact to nonlinear inhomogeneous thin rods). The main result: The existence of an ``associated group'' that allows us to consider applications of the non- iterative transformation method. The ordinary differential equation related to the model in point is invariant with respect to the stretching group of transformations. The author presents the numerical results (numerical methods of integration are used) which stems from the group properties (the obtained numerical results are directly validated by integrating the ordinary differential problem as an initial one).