This paper presents an eddy current loss analysis for a transverse flux rotary machine (TFRM) with laminated stator cores, which consist of inner and outer cores whose laminated directions are perpendicular to each other. Although the TFRM is laminated to reduce eddy current losses, it still exhibits rapidly increasing core losses as the frequency increases. To solve this problem, slits are introduced to the stator outer core. 3-dimensional finite element analysis (3D FEA) based on the T-${Omega}$ formulation is used to solve the eddy-current problem for a various numbers of slits in the nonlinear lamination core. The effects of the slits are confirmed using experiment data and 3D FEA results.