Using a modified 3D random representative volume(RV)finite element model,the effects of model dimensions(impact region and interval between impact and representative regions),model shapes(rectangular,square,and circular),and peening-induced thermal softening on resultant critical quantities(residual stress,Almen intensity,coverage,and arc height)after shot peening are systematically examined.A new quantity,i.e.,the interval between impact and representative regions,is introduced and its optimal value is first determined to eliminate any boundary effect on shot peening results.Then,model dimensions are respectively assessed for all model shapes to reflect the actual shot peening process,based on which shape-independent critical shot peening quantities are obtained.Further,it is found that thermal softening of the target material due to shot peening leads to variances of the surface residual stress and arc height,demonstrating the necessity of considering the thermal effect in a constitutive material model of shot peeing.Our study clarifies some of the finite element modeling aspects and lays the ground for accurate modeling of the SP process. Using a modified 3D random representative volume (RV) finite element model, the effects of model dimensions (impact region and interval between impact and representative regions), model shapes (rectangular, square, and circular), and peening-induced thermal softening on resultant critical quantities (residual stress, Almen intensity, coverage, and arc height) after shot peening are systematically examined. A new quantity, ie, the interval between impact and representative regions, is introduced and its optimal value is first determined to eliminate any boundary effect on shot peening results.Then, model dimensions are respectively assessed for all model shapes to reflect the actual shot peening process, based on which shape-independent critical shot peening quantities are obtained. Future, it is found that thermal softening of the target material due to shot peening leads to variances of the surface residual stress and arc height, demonstrating the necessity of considering the thermal effect in a constituion tive material model of shot peeing. Our study clarifies some of the finite element modeling aspects and lays the ground for accurate modeling of the SP process.