Microindentation methods are commonly used to determine material properties of soft tissues at the cell or even sub-cellular level. In determining properties from force-displacement (FD) data, it is often assumed that the tissue is initially a stress-free, homogeneous, linear elastic half-space. Residual stress, however, can strongly influence such results. In this paper, we present a new microindentation method for determining both elastic properties and residual stress in soft tissues that, to a first approximation, can be regarded as a pre-stressed layer embedded in or adhered to an underlying relatively soft, elastic foundation. The effects of residual stress are shown using two linear elastic models that approximate specific biological structures. The first model is an axially loaded beam on a relatively soft, elastic foundation (i.e., stress-fiber embedded in cytoplasm), while the second is a radially loaded plate on a foundation (e.g., cell membrane or epithelium). To illustrate our method, we use a nonlinear finite element (FE) model and experimental FD and surface contour data to find elastic properties and residual stress in the early embryonic chick heart, which, in the region near the indenter tip, is approximated as an isotropic circular plate under tension on a foundation. It is shown that the deformation of the surface in a microindentation test can be used along with FD data to estimate material properties, as well as residual stress, in soft tissue structures that can be regarded as a plate under tension on an elastic foundation. This method may not be as useful, however, for structures that behave as a beam on a foundation.