In this paper, we have proposed an algorithm for building a hierarchical 3D mesh model of heterogeneous media, native or human-made, described by a stack of cross-section 2D images obtained via digital imaging methods, such as magnetic resonance imaging (MRI), computed tomography (CT), etc. The algorithm yields a multi-level hierarchical mesh accurately capturing the complex internal geometry of the medium at the micro-level. The meshes are oriented towards the modern nonconforming multiscale finite element methods. We have provided a validation of the algorithm in a test medium containing microinclusions of various geometric shapes. To simulate the output data of CT non-destructive imaging, we have generated the stack of slice images of the test media concerned. We have obtained the accuracy estimations for the volume fraction of inclusions and the interface surface area. We also have shown the scalability of the algorithm proposed using OpenMP technology.