The influence of the mismatch effect on thin ferroelectric film properties has been studied in the phenomenological theory framework. The polarization dependent part of the surface energy that defined the boundary conditions for the Euler-Lagrange differential equation was written as a surface tension energy. The latter was expressed via the surface polarization and the tension tensor related to the mismatch of the substrate and film lattice constants and thermal expansion coefficients. The interfacial strain caused by the mismatch effect induces the additional surface polarization P-m via a piezoelectric effect that arises near the surface in any film. The new parameter P-m/P-S (P-S is the known value of the spontaneous polarization in the bulk ferroelectric material at T = 0 K) appeared in the derived phenomenological equations. So we calculate the influence of the parameter P-m/P-S on the depth distribution of the dimensionless film polarization P/P-S, its dependence on temperature, film thickness and applied electric field, as well as that on the hysteresis loop shape, coercive field values, phase diagram and average dielectric susceptibility temperature dependence. Non-zero P-m/P-S values cause a mismatch induced thickness dependent internal electric field E-m. We have shown that this field drastically influences all the properties. In particular, the polarization profile becomes asymmetrical, the polarization temperature dependence resembles that in the external electric field and there is a possibility of external field screening by the internal field E-m. The asymmetry obtained for the hysteresis loop suggests that it is possible that the self-polarization phenomenon recently observed in some films is related to the mismatch effect. The thickness induced ferroelectric-paraelectric phase transition has been shown to exist when \P-m\/P-S < 1. A large enough ratio \P-m\/P-S > 1 could be the physical reason for the ferroelectric phase conservation in ultrathin film. The possibility of observing the peculiarities of the film property temperature and thickness dependences related to the mismatch effect is discussed.