Investigation of a fourth order Euler-Bernoulli partial differential equation governinga simply supported beam with point load is done analytically by using the Diracdeltadistribution for both homogeneous and non-homogeneous (forced) vibration.A solution is derived and plotted for the first five modes. A finite element methodis implemented for numerical solution of the resulting differential equation system.The solution of the differential equation system is implemented by the Newmark-Beta method. The results from the analytical solution and the numerical methodare logically matching. Experiments with stochastic load is also performed.