In this paper, a plane Mode-I central semi-permeable crack in a piezoelectric strip of finite width is studied, where different strip-like mechanical yielding and electrical saturation zones are considered in front of crack tips. Dependence of the strip-like zone-lengths and the electric displacement inside crack on the width of the piezoelectric strip and the external electrical and mechanical loads is explored. By using integral transform and Copson method, the formed mixed boundary value problem is transformed into the second kind Fredholm integral equations. For the different cases where the zone size of mechanical yield is greater than, less than, or equal to the electrical saturation, the nonlinear zone sizes are formally obtained, which reduce to the analytical solutions of an infinite piezoelectric plane in literature, when the width of piezoelectric strip approach infinity. With numerical discretization and the bisection iteration, the external loads and electric displacement inside crack corresponding to the chosen sizes of the nonlinear zone can be numerically solved for the case of finite width. Selected numerical examples are presented. Results indicate that the electrical load enhances the electrical displacement inside crack, but the mechanical load reduces it. The predicted zone length of electrical saturation, no matter it is longer or shorter than mechanical yielding zone, is always dependent on external electromechanical loads under the semi-permeable crack condition. The electrical load always promotes the mechanical yielding zone size, while the effect of the mechanical load on the electrical saturation zone, i.e., promoting or preventing, rely on the relative size of the nonlinear zones. In addition, the strip-like zone-lengths and the electric displacement inside crack decrease as the width of the strip increases.