The elastic strain state in a 25 nm (In,Ga)As epitaxic film deposited on a (001) GaAs substrate includes a Poisson expansion perpendicular to the interface. This creates a tetragonally distorted lattice in the film which shifts high-order Laue-zone (HOLZ) lines in electron channeling patterns (ECP) from the film compared to ECP's from pure GaAs. The line shifts are predictable, thereby allowing measurement of elastic strains parallel and perpendicular to the film/ substrate interface independently. The technique appears to have an accuracy close to 0.2%.