Any technological process and technology aims a quality and precise product, something almost impossible without high rigidity machine tools, equipment and components. Therefore, from the design phase, it is very important to create structures and machines with high stiffness characteristics. At the same time, increasing the stiffness should not raise the material costs. Searching this midpoint between high rigidity and minimum expenses leads to investigations and checks in structural components through various methods and techniques and sometimes quite advanced methods. In order to highlight some aspects concerning the significance of the mechanical equipment rigidity, the finite element method and an analytical method based on the use Mathcad software were used, by taking into consideration a subassembly of a grinding machine. Graphical representations were elaborated, offering a more complete image about the stresses and deformations able to affect the considered mechanical subassembly.