Syringe pump has been applied to actuate soft pneumatic robots. Most previous works focus on designs of the syringe pump, its applications, and improvement of its problems such as leaking air, inefficient motions, etc. This paper introduces dynamical modeling and parametric analysis of a syringe pump. The syringe pump is made of a commercial syringe and a linear actuator. The dynamic equation is derived from the motions of the linear actuator, the air dynamics in the syringe, and the airflow inside the soft actuator. Because of the high-elastic materials, the volume of the soft actuator is a time-varying parameter. Therefore, the variation of volume is estimated by the Kalman filter instead of relying on the traditional design method. The dynamic model is also utilized to select optimal parameters which are verified by the experiments for the syringe pump. Two system controllers are designed with and without consideration of the pressure dynamics. The controller considering pressure dynamics outperforms. This work shows the benefits of pressure dynamic of the syringe pump for both system design and advanced controller design.