A method for determining the dynamic response of prismatic damped Euler–Bernoulli beams subjected to distributed and concentrated loads is presented. The method yields exact solutions in closed form and may be used for single and multi-span beams, single and multi-loaded beams, and statically determinate and indeterminate beams. Also Green functions for various beams with different homogenous and elastic boundary conditions are given. In order to demonstrate the use of the Green functions method, several examples are given. Some of the obtained results are compared with those given in the references.