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This article introduces a recovery approach for a snake robot with multiple failed joints. The operational environments of snake robots are expected to cause high loads on the robot actuators, which may lead to the actuator malfunction problem. To solve this issue, we propose a recovery approach that enables a snake robot to restore its body shape to be close to its targeted form before failure. The restored body shape helps the robot to carry out the desired locomotion gait. To achieve this objective, we utilize the hyper-redundancy of a snake robot by controlling the adjacent joints of the failed one to form a so-called recovery part. This part of the robot works to eliminate the effect of the failed joint and reform the robot's shape. We extend our concept for a snake robot with multiple joint-failure by forming multiple recovery parts corresponding to the failed joints. We consider locked, free, and partially failed joint types. To compensate for the movement of failed joints, we propose a kinematic-based controller considering 2-D and 3-D shape-based motion gaits. We applied the proposed approach experimentally for three motion gaits, namely lateral undulation, sidewinding, and crawler gait. Several multiple failed-joint cases were considered, with different combinations of failed joints. The results showed the validity of the proposed method to eliminate the joints' failures effect, and thus, the robot can carry out the desired motion successfully.