This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model's curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface's parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work.