A new model is proposed to explain the magnetostriction effects in ferrimagnetic spinels and garnets with Mn3+, Co2+, and Fe2+ ions substituted into octahedral sites. Considerable experimental evidence has revealed that small amounts of each of these ions will alter substantially the magnitude of either the λ100 or λ111 magnetostriction constant, depending on the particular ion. The theory is based on the concept that Jahn-Teller effects produce local site distortions of tetragonal (favoring 〈100〉 axes) or trigonal (favoring 〈111〉 axes) symmetry which are able to switch among the different axes of the particular family in order to select the axis closest to the direction of the magnetic field. For Mn3+ ions, the local site distortions are expected to be tetragonal (c/a≳1), in accordance with observations in a variety of magnetic oxides where static cooperative effects are present and will produce large positive changes in the λ100 constant. With Co2+ ions the distortion is also tetragonal, but of the opposite sign (c/a<1) (consistent with cooperative effects in CoO) and will produce large negative changes in λ100. In the case of Fe2+ ions, the distortion is trigonal (α<60°), as evidenced by its behavior in FeO, and will produce large positive changes in the λ111 constant. In each case reviewed, the theoretical results are in complete agreement with the available room-temperature magnetostriction-constant data on a qualitative basis. An estimate of the magnitude of the elastic energy of the local site distortion suggests that crystal-field energy-level splittings required to create the observed magnetostrictive effects are only on the order of 10−2 cm−1.