The aim of this paper is to consider the necessity of introducing the generalized functions for the construction and solving mathematical models. Mathematical models in mechanics have been usually given by a partial differential equation with some boundary and initial conditions. With regards to the construction of a mathematical model the following remarks are worthy of mention: First we have to catch sight and then to select the basic elements of the situation (of the object) we wish to model. Consequently, a mathematical model is only an approximation of the object to which it corresponds.