Lightweight design has led to an increased use of materials with complex microstructures such as porous metals or ceramics or 3D printed lattice structures. It also favors optimized complex component shapes which can only be produced by 3D printing, casting or injection molding. Their mechanical properties may be sensitive to undesired microstructural features such as porosity which are inherent in these production methods. As a consequence, there is an increased need for micromechanics simulations to determine the effective mechanical properties of materials and components with cellular and porous microstructures. Classical FEM simulation may not always be a feasible approach because it requires the generation of geometry conforming meshes which must be fine enough to capture all relevant geometric details on the one hand, but coarse enough to keep the effort for mesh generation and computation at a practical level on the other hand. Recently, immersed-boundary finite element methods have been used to overcome the meshing problem. Such methods do not require the generation of a boundary-conforming mesh and are suited for the simulation of arbitrarily complex domains. This approach is implemented in the Structural Mechanics Simulation module of VGSTUDIO MAX by Volume Graphics and works directly on CT scans which accurately represent complex material structures and internal discontinuities. This simulation approach was validated against both experimental tests and a classical FEM simulation. A comparison between experimental and simulated results of tensile tests was conducted for two types of additively manufactured AlSi10Mg components, a tension rod and a bionically optimized aeronautic structural bracket, showing a good correlation between the predicted and measured tensile strengths and the locations of the first crack occurrences. For a solid cube and a cubic lattice made from Ti6Al4V, the simulated effective Young’s modulus and the maximum local stress were in good agreement between this simulation approach and a classical FEM simulation. The simulation approach presented here provides an easy-to-use and validated method for the determination of stress distributions and displacements in material probes or components with cellular, porous or otherwise complex microstructures under external loads. It can be used to determine the effective elastic properties for static loads and to serve as an input for the assessment of material fatigue behavior.