Filling dielectric porous matrices, particularly anodic aluminum oxide, with metal confers a promising solution for nanocomposite creation. In this regard, the problem of estimating and predicting the physical and mechanical properties of such materials is of prime importance. The present work focuses on the numerical modeling of the effective and ultimate stress-strain (under compression) characteristics of nanocomposites based on anodic aluminum oxide with unidirectional filamentary pores filled with different metals (In, Sn, and Zn). The dependences of the tensor components of the effective elastic moduli, coefficients of elastic anisotropy (in different directions), and compression strength (along the nanowires) on the structure parameters and the concentration of nanowires are investigated.