The loaded tooth contact analysis of cycloid drives based on the traditional rigid body or constant contact stiffness method typically assumes perfect geometries without backlash. This model lacks the ability to include tooth profile modification effect accurately. In this study, a quasi-static approach is presented for analyzing the load distribution characteristics of the cycloid drive with tooth profile modification based on the proposed Hertzian contact stiffness method. Firstly, the unloaded tooth contact analysis is applied as a preprocessor to determine the positions of contact points, backlash between the cycloid gear teeth and rollers, and rotational angle of the cycloid gear within a mesh cycle. The analysis yields the unloaded transmission error. Secondly, in the load distribution analysis, the Hertzian contact stiffness method implemented by an iterative numerical calculation procedure is proposed. Due to the statically indeterminate structure of the multi-tooth contact, a varying nonlinear contact stiffness that depends on the load and contact geometry is considered to establish the relationship between the load and deformation. The proposed method is also compared with the two traditional methods. Finally, a detailed parametric study is presented applying all three methods to demonstrate the influence of the tooth profile modifications on the backlash, load distribution, contact stiffness, loaded transmission error and real contact ratio of the cycloid drive. This study gives an in-depth understanding of the tooth contact and load distribution characteristics of cycloid drives with tooth profile modifications and therefore can be employed to assist gear design.