Mathematical model for skeleton stress-strain curve under dynamic loading (SSSC) is one important issue to study the dynamic behavior of soft soil. Based on mechanism of developing process, primary mathematical behavior that SSSC model should meet is analyzed. Mathematical investigation on two conventional SSSC models, namely hyperbolic model and exponential model, is conducted. Dynamic stress index is proposed and employed to signalize the shortcomings of two conventional models. A composite tangent-exponent model for SSSC with three parameters is established, which is a monotone increasing and up limited function. The new model can overcome conventional shortcomings. Finally, good agreement between investigated and new model fitted data has been found out.