Resistive singular layer equations are developed by applying the magnetohydrodynamic (MHD) model to toroidal anisotropic plasmas. This work extends the previous ideal MHD theory [Shi et al. Phys. Plasmas 23, 082121 (2016)] to the resistive case. These layer equations can be used to investigate resistive localized MHD instabilities, such as tearing instability and resistive interchange instability. Compared to existing resistive theory [Johnson and Hastie, Phys. Fluids 31, 1609 (1988)], our model includes plasma compressibility, allowing for a study of the coupling between parallel motion to perpendicular one, which is known as the apparent mass effect. In addition, these obtained equations are valid for low n modes, where n is the toroidal mode number. The dispersion relation is derived in a reduced model. We find that the anisotropic pressure effect (when p⊥ > p‖) not only increases the stable threshold of the resistive interchange mode but also raises the critical value Δc of the tearing mode stability index Δ′, which represents the logarithmic jump of the radial magnetic field perturbation across the rational surface. This discovery holds significant practical implications for mitigating neoclassical tearing modes in high confinement plasmas, particularly those characterized by a low aspect ratio (such as spherical tokamaks) or low magnetic shear (as designed in ITER hybrid scenarios). However, it enhances the growth rate of the tearing mode in a low growth rate region, where p‖ and p⊥ denote the pressure components parallel and perpendicular to the magnetic fields, respectively.