The fine-blanking process is used in the production of automobile parts and other metal components. Although the fine-blanking process can produce sheared surfaces with higher precision than the punching process, shear droops on cut surfaces are also formed, as in the punching process. It is important to determine the causes of the formation of shear droops, but the mechanism is difficult to determine experimentally. Here, the finite element method (FEM) is adopted to study the causes of the formation of shear droops. The cut surfaces in the present experiments have fine sheared surfaces but no fracture surfaces. Although a combination of the fracture criterion and element-kill method is used for many simulations of the fine-blanking process, fine sheared surfaces cannot be evaluated by the combination of these methods. In the present calculations, an adaptive remeshing technique for FEM is used to create fine sheared surfaces. The shear droop is associated with the initial compression by and the subsequent clearance of the punches and dies. Results are obtained for various clearances and initial compressions in the fine-blanking process for high-strength steel, and the experimental and calculation results are compared. In the present paper, we show that the shear droops are affected by the clearance of and initial compression by the punches and die.