Anisotropic theoretical models of critical current and AC loss of high temperature superconducting (HTS) tape in both DC and AC background fields were established based on the effective mass theory (the anisotropy Ginzburg—Landau theory) and the critical state model (CS model). A formula to describe the relationship between critical current and stress/strain was proposed by use of the definition of irreversible strain. The relation between AC loss and stress/strain was developed based on the critical current-strain relation and Norris’ formula. A numerical model to calculate AC loss of HTS coil was developed from the anisotropy theory of AC loss and critical current of short sample.