In the present work, a shrink fit consisting of a linear isotropic hardening hub and a plastic orthotropic hollow inclusion is considered. The orthotropic plastic flow is governed by a particular version (Durban, D. (1986). Radial Stressing of Thin Sheets with Plastic Anisotropy, Int. J. Mech. Sci., 28: 801) of the anisotropic flow rule proposed by Hill, R. (Hill, R. (1979), Theoretical Plasticity of Textured Aggregates, Math. Proc. Camb. Phil. Soc., 85: 179), along with a linear hardening characteristic. The isotropic plastic flow is based on the Tresca's yield condition and its associated flow rule. In this study, the closed-form expressions for the displacements and the stresses in each of the plastic zones are presented. Some numerical results are given to significantly show the influence of the degree of plastic orthotropy on the interference, the interface pressure, and the elastic-isotropic plastic interface radius.