Surveys of microgeodetic networks (apertures of a few kilometres or less) using relatively simple, inexpensive commercially available equipment are capable of measuring Earth strains of 2 × 10−6 or greater. Use of such networks for strain measurements offers many practical advantages over larger networks. Trilateration alone achieves virtually the same precision as combined trilateration and triangulation, with the expenditure of significantly less time and energy. Strain determinations can be made by estimating coefficients in low order polynomial expansions of the strain in the network. The technique uses the theory of generalized inverses for rectangular matrices to estimate polynomial coefficients.This method is used to investigate the resolution of microgeodetic networks using a com prehensive suite of synthetic data. Real data from a network in Peru show that a shear strain event of −3 microstrains occurred within this network during the period 1975–1976. A further shear strain event of +3 microstrains occurred during 1976–1978, possibly as a response to the first.