The stress-related problem is a very common problem in engineering practice.Many theoretical studies as well as the engineering applications for solving this problem have been developed.It has been known, however, that this kind of problem is very challenging since several difficulties must be overcome in order to solve it effectively.Traditionally,SIMP (Solid Isotropic Material with Penalization) method is often employed to tackle this kind of problem.Although remarkable achievements have been made within this computational framework, however, there are still some issues that have not been well addressed.Based on this background, in the present work, stress-related topology optimization problems were investigated via level set approach, a different topology optimization framework from SIMP.Our research indicated that some of the numerical difficulties encountered in the process of stress-related topology optimization are due to the ill-posedness of the problem formulations.In order to cure the pathological phenomena, in the present paper,regularized formulations for stress-related topology optimization problems are proposed and the corresponding numerical solution aspects are discussed.Thermal stress-related topology optimization problems are also solved as an extension application to the regularized formulations in our paper.Furthermore, considering a general observation of the stress concentration problem is that certain geometric shapes with large curvature can cause stress concentration, we also present a shape and topology optimization approach for stress concentration problem by applying geometric attribute with a global form objective.Numerical examples show that under regularized problem formulations, level set approach is a promising tool for stress-related topology optimization problems.