The shearing machine is a critical equipment for spent fuel reprocessing. Under extreme conditions, the stainless steel roller components in the shearing machine may get stuck, resulting in rolling friction becoming sliding friction. The limited lubrication in the high-radiation environment results in severe wear on the contact surfaces, greatly reducing the equipment’s service life. Therefore, it is crucial to predict the wear of the roller components. To address the difficulties in predicting wear, an orthogonal experiment with three factors and five levels was carried out on reciprocating dry friction wear of stainless steel. The nonlinear relationship between various factors (load, speed, time) and the wear coefficient was determined through range and variance analyses. A prediction model for the dry friction wear coefficient of stainless steel was proposed by combining the above experimental data. Comparative experiments were conducted and the results indicate that the model has high accuracy and effectiveness.