In the numerical analysis of mechanical structures, rigidity plays an important role of reducing the computational complexity. Two strategies are employed in the literature: Either parts of the structure are modeled as rigid throughout the entire simulation, see e.g. [5] or parts of the structure switch between rigid and flexible or vice versa, see e.g. [3]. To determine whether certain parts can actually be considered rigid, the stresses in the rigid domains must be analyzed. Contrary to intuition, stresses in rigid bodies and inclusions are neither zero nor indeterminate but can be determined by equilibrium equations. While this is well known in structural mechanics for the computation of stress resultants in statically determinate frame structures, this is rarely considered in continuum mechanics for stresses. Only Grioli [1] as well as Fosdick and Royer-Carfagni [2, 4] developed theoretical concepts for stresses in rigid bodies but neither provided a numerical method nor computational results. In contrast, Bessonov and Litvinova developed a numerical method for the stress computation in rigid domains [6]. However, it is limited to purely rigid structures. Thus, it is unable to compute stresses in rigid parts connected to elastic material. In this talk, we present a novel two-step numerical method to compute the stresses in rigid parts that may be connected to non-rigid parts with arbitrary constitutive relations. It is capable of computing the stresses for arbitrary geometry and topology of the rigid bodies and inclusions. Additionally, it can be applied both in the geometrically linear as well as the nonlinear regime. In the method, the rigidity is enforced by multi-point constraints. For efficiency reasons, the constraints are applied using a master-slave elimination scheme [7]. The method is verified using analytical solutions from structural analysis as well as approximate solutions in continuum mechanics. Additionally, implementation aspects are discussed. [1] G. Grioli. Meccanica (1983), 18:3–7 [2] R. Fosdick and G. Royer-Carfagni. J Elast (2004), 74:265–276 [3] B. Göttlicher and K. Schweizerhof. Comput Struct (2005), 83:2035–2051 [4] R. Fosdick and G. Royer-Carfagni. J Elast (2007), 87:211–238 [5] P. Areias et al.: Int J Comput Methods Eng Sci Mech (2019), 20:494–513 [6] N. Bessonov and Y. Litvinova. In H. Altenbach et al. (ed.), Progress in Continuum Mechanics (2023), 91–112 [7] J. Boungard and J. Wackerfuß. Comput Mech (2024), 74:955–992