Surface immobilized enzymes play a key role in numerous biotechnological applications such as biosensors, biofuel cells, or biocatalytic synthesis. As a consequence, the impact of adsorption on the enzyme structure, dynamics, and function needs to be understood on the molecular level as it is critical for the improvement of these technologies. With this perspective in mind, we used a theoretical approach for investigating local protein flexibility on the residue scale that couples a simplified protein representation with an elastic network and Brownian dynamics simulations. The impact of protein adsorption on a solid surface is implicitly modeled via additional external constraints between the residues in contact with the surface. We first performed calculations on a redox enzyme, bilirubin oxidase (BOD) from M. verrucaria, to study the impact of adsorption on its mechanical properties. The resulting rigidity profiles show that, in agreement with the available experimental data, the mechanical variations observed in the adsorbed BOD will depend on its orientation and its anchor residues (i.e., residues that are in contact with the functionalized surface). Additional calculations on ribonuclease A and nitroreductase shed light on how seemingly stable adsorbed enzymes can nonetheless display an important decrease in their catalytic activity resulting from a perturbation of their mechanics and internal dynamics.