The cytoskeletal activity of motile or adherent cells is frequently seen to induce detectable displacements of sufficiently compliant substrata. The physics of this phenomenon is discussed in terms of the classical theory of small-strain, plane-stress elasticity. The main results of such analysis is a transform expressing the displacement field of the elastic substrate as an integral over the traction field. The existence of this transform is used to derive a Bayesian method for converting noisy measurements of substratum displacement into "images" of the actual traction forces exerted by adherent or locomoting cells. Finally, the Monte Carlo validation of the statistical method is discussed, some new rheological studies of films are presented, and a practical application is given.
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