In metal rolling processes, internal holes or cracks can result in unqualified products. This paper evaluates the possibility of cracking in three-roll planetary rolling of bismuth-containing stainless steel bar by combining experiments, finite element simulations, and theoretical modeling. Stress-strain data obtained from hot compression experiments were used to draw hot processing maps after modification. The prediction results of several standard ductile fracture criteria were compared, and it was found that the Ayada criterion could accurately predict the size and location of rolled section cracks during the rolling process. The study also investigated the effects of three key forming parameters: billet temperature, strain rate, and friction coefficient on the percentage of damaged area. Results showed that billet temperature had a significant influence on crack initiation followed by strain rate. A mathematical model with damage value as its target was established using a three-way cubic polynomial regression analysis for these parameters' interaction effect on crack initiation and development. By calculating extreme values for this function based on optimized process parameters, a set of optimum processes with minimal risk for initiation cracking was obtained. Field rolling results confirmed no cross-sectional cracks according to these optimized process parameters.