The tearing-mode instabilities of Harris sheet magnetic field configuration are studied based on the numerical simulations of two-dimensional, resistive, compressible MHD models with isotropic pressure. The linear growth rate and the eigenmode structure are calculated from the linear numerical model for various parameters: magnetic Reynolds number, Rm; the ratio of wavelength to the layer thickness; magnetic By component; and plasma beta, as well as for different equations of state. The linear solutions are then used as initial perturbations of the nonlinear numerical model to allow the full evolution of resistive tearing-mode instability. The linear calculations show that for the range of Rm=10-105 the fastest growth rate increases with decreasing Rm and only slightly increases with increasing plasma beta and By but that it is not sensitive to the equation of state. While the nonlinear calculations show that only for large Rm, where the diffusion time is much larger than the linear growth time, the magnetic island may possibly grow substantially and become saturated. For small Rm the plasmoids either diminish in the late stage or do not have apparent growing; that is, the linear analysis is not meaningful for large resistivity cases. The calculations are compared to the magnetic island structure at Earth's magnetopause reconstructed from the single-spacecraft data by Hau and Sonnerup [1999>. ¿ 2001 American Geophysical Union