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It’s essential to establish a dynamic model of flexible multi-link mechanism with clearance for ultra-precision press to analyze its dynamic response. Traditionally, the rigid model of multi-link mechanism often neglects the effect of revolute and spherical clearance joints, and flexibility of crank shaft and linkage, which reduces the analysis precision. To investigate its dynamics more accurately, an improved dynamic model of flexible multi-link mechanism with clearance was established, which considered the effect of revolute and spherical clearance joints, and flexibility of crank shaft and linkage. It was demonstrated that the revolute and spherical clearance affected the dynamic response of the mechanism dramatically and the motion of the crank shaft center and ball center of spherical joint were mainly characterized by only two phases: free flight and impact motion. In addition, the influence of the clearance size and speed of crank shaft on the dynamic characteristics of the multi-ink mechanism was also investigated. The results showed that with the increase of the clearance size, the position of the slider’s lower dead center was moved up simultaneously, the peak values of velocity and acceleration were decreased to a minimum and then increased with the increase of clearance size and speed. With the increase of crankshaft speed, the position of the slider’s lower dead center and the maximum deviation value were also increased gradually, and the values of velocity and acceleration were increased significantly.