<p>We use Suo’s complex variable formulation to derive a closed-form solution to the plane strain problem of a compressible liquid inclusion of arbitrary shape embedded in an infinite degenerate orthotropic elastic matrix subjected to uniform remote in-plane stresses. The one-to-one mapping function that maps the exterior of the liquid–solid interface onto the exterior of the unit circle in the image plane contains an arbitrary number of terms. Using a varied form of analytic continuation, a set of linear algebraic equations with quite simple structure is obtained. Once the set of linear algebraic equations is solved, the internal uniform hydrostatic stress field within the compressible liquid inclusion and the elastic field in the degenerate orthotropic elastic matrix characterized by a pair of analytic functions are completely determined.</p>