Servo presses are widely used in high-precision, complicated forming process fields and promoted around the world in recent years. It is the trend of forging machinery for its servo motor-based digital heavy haul driven technology. At present, it becomes the hot research field. The structure characteristics of triangular elbow servo press were firstly introduced in the paper. And then the kinematics mathematical model of triangular elbow transmission mechanism was deduced and given. Based on it, this paper provides the slider kinematics analysis by Matlab. The slider motion law under various parameters can be analyzed and compared. The results would be useful reference for optimization design of transmission mechanism. The case study provides more visual and reliable decision basis for designer.