We present analytical models and experimental results to describe low-defect density growth (∼ 6 × 105/cm2) of highly mismatched antimonides on Si and GaAs substrates, with strain relief achieved at the growth interface through periodic, 90° interfacial misfit dislocations (IMF). We use molecular mechanics (MM) based modeling techniques to understand, at the atomic level, the spontaneous formation and energetics of these IMF. We have modeled, grown and characterized two systems extensively, these are - AlSb on Si with ∼ 13% mismatch and GaSb on GaAs with 7.83% lattice mismatch. Growth of these materials by molecular beam epitaxy (MBE) and subsequent High-Resolution Transmission Electron Microscopy (HR-TEM) has indicated that there is no tetragonal distortion in these two systems despite the high lattice mismatch. Instead, the mismatched epi-layers spontaneously form periodic IMF arrays that run along both  and [1-10] directions and relieve almost 100% of the strain in a few monolayers of deposition. To model this form of strain relief, we use existing theories of strain relief adapted for very high strain conditions and we also use bond energetics to model the strain-relieving interface. The IMFs in these systems are periodic and so is the deviation in bond lengths and bond angles, which restricts our calculation space to a finite number of elements. We shall also demonstrate extensive growth and characterization results of the materials grown with a particular emphasis on the strain-relieving interface to show excellent agreement of the experimental data with the proposed models. The high quality and low-defect density in AlSb grown on Si, has helped us demonstrate optically pumped IR VCSELs and edge emitters monolithically on Si (001) and this data will also be presented.