This work deals with the mechanical response of a simple composite structure subjected to an impact with low velocity and large mass. The main aim is to simulate the dropped tools taking into account scattering of various parameters of the system. The measured mechanical responses were modeled by using empirical polynomial forms resulting from a design of experiments. In a first step, the polynomial of the contact force between the striker and the structure was used by assigning to each variable a statistical distribution. In a second step, a distribution was attributed to the coefficients of the polynomial. Finally, the Monte-Carlo technique was used to calculate a failure probability on the basis of the action—resistance modeling. This work also serves the purpose of helping the engineering and design departments to carry out an accurate reliability analysis on the behavior of impacted composite structures.