  Biological cells in soft materials can be modeled as anisotropic force
contraction dipoles. The corresponding elastic interaction potentials are
long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic
constants, geometry and cellular orientations. On elastic substrates, the
elastic interaction is similar to that of electric quadrupoles in two
dimensions and for dense systems leads to aggregation with herringbone order on
a cellular scale. Free and clamped surfaces of samples of finite size introduce
attractive and repulsive corrections, respectively, which vary on the
macroscopic scale. Our theory predicts cell reorientation on stretched elastic
substrates.
