Maintaining and restoring robot balance in the presence of external disturbances is a significant capability for a quadruped robot. This is due the fact that these robots move over uneven terrains which may be themselves the sources of the disturbances. In this article, the balance recovery problem of a quadruped robot after an external disturbance will be investigated. To this end, as first stage, the equations of motion of a whole-body model of a robot and also a constraint elimination method will be proposed. In order to recover robot balance, the desired accelerations will be computed based on the concepts of a PD controller and by using the desired velocities and the positions of the main body. However, these accelerations maybe lead to slip stance feet or lose robot stability. Therefore, an optimization problem will be defined to calculate the admissible accelerations and the contact forces simultaneously. The optimal regulation of the contact forces will be done to distribute the contact forces among all stance legs to avoid feet slippage. Since the stability and the slippage avoidance conditions are formulated as linear constraints, the optimization can be solved as a linear constrained least squares error. To evaluate the effectiveness of the proposed algorithm, it will be examined on a quadruped robot in the simulation in two different case studies: in standing situation and walking gait. Finally, obtained results will be discussed.