A theoretical model of magneto-acoustic current imaging is derived, based on fundamental equations of continuum mechanics and electromagnetism. In electrically active tissue, the interaction between an applied magnetic field, B, and action currents, J, creates a pressure distribution. In the near field limit, this pressure obeys Poisson's equation, with a source term (delta x J).B. The displacement and pressure fields are calculated for a dipole (q), oriented either parallel or perpendicular to the applied magnetic field (B), at the center of an elastic, conducting sphere (radius a, shear modulus G). Surface displacements are on the order of qB/(4 pi Ga), which is about 1 nm for typical biological parameters. If the applied magnetic field is changing with time, eddy currents induced in the tissue may be larger than the action currents themselves. The frequency of the pressure and displacement arising from these eddy currents, however, is twice the frequency of the applied magnetic field, so it may be possible to eliminate this artifact by filtering or lock-in techniques. Magneto-acoustic and biomagnetic measurements both image delta x J in a similar way, although magneto-acoustic current imaging has the disadvantage that acoustic properties vary among tissues to a greater degree than do magnetic properties.