A new research method of spiral climbing based on screw theory and the elastic envelope for the snakelike robot with orthogonal joints was presented． Firstly， the screw theory was used to build kinematics modeling of snakelike robot to reduce the complexity of D-H modeling method． Secondly， the contact relationship between the snakelike robot and cylindrical rod during the climbing movement was analyzed based on the screw theory，and a binary images representation was proposed to reveal the elastic envelope state between snakelike robot and cylindrical rob． Finally，based on the analysis results of elastic envelope， the spiral climbing force of the snakelike robot was obtained，and then the parameter control optimization model with safe climbing force and climbing coefficient as the optimization target was proposed． The simulation results show that the climbing force and the elastic envelope state are consistent，which verifies the optimization model．