For several years, manufacturers are tending towards the massive use of robots in order to increase the precision of certain manipulations and on the other hand to improve their productivity. This is why, several activities such as handling, assembly, welding, painting, etc… have been attributed to these robots. Thus, to be able to simulate its behavior or to control a robot according to the needs of its operation, it is necessary to go through the first step, which is its modeling. This chapter presents the necessary steps and methods to follow in order to develop the dynamic model of any robot manipulator (open chain, serial). These robots have been constructed to be mechanically rigid, but due to their fast movements, the low flexibility of the articulations may affect their activities. For this reason, the proposed model will consider the flexibility of the joints. Three springs are integrated to model the joint elasticity, as well as the flexibility of the axes between the driven bodies and the output shafts of the gearboxes, and the meshing phenomenon inside the gearbox transmissions. The proposed dynamic model is developed based on Denavit-Hartenberg Modified (DHM) method and using the Euler-Lagrange approach. Therefore, the purpose of this work is to study the effect of the joints flexibilities on the robot behavior.