Coral sands are commonly used in hydraulic fill foundations and as subgrade fill in the construction of islands and reefs. The stress paths followed by soil consolidation or filled subgrade are characterized by K0 consolidation or constant stress ratio stress path. It is necessary to develop a computational model that reflects the effect of stress path on deformation in order to accurately estimate soil deformation during the filling process. Based on the generalized Hooke's law, a nonlinear elastic model in the form of a power function is proposed to describe the stress-strain curve of coral sand, and the functional expression is given. A series of K0 consolidation tests and drained triaxial compression tests with a constant stress ratio path were conducted on the coral sand to investigate the stress-strain curves and the behavior of particle breakage. The applicability of the power-law stress-strain model for the coral sand under the earth fill stress path was investigated, and the calculated results of the model were compared with the test curves. The results show that the stress-strain curves under both K0 consolidation and constant stress ratio paths conform to the form of power-law curves and can be described by a power-law nonlinear elastic model. The tangent modulus and tangent Poisson's ratio of this model can be expressed as a function of axial effective stress and can be determined by parameters related to the stress increment ratio or K0 coefficient. Under a constant stress ratio path, the tangent Poisson's ratio and tangent modulus increase with the increase of the axial effective stress. For the same axial effective stress condition, a large stress ratio corresponds to a large tangent modulus and a small tangent Poisson's ratio. With the increase of the axial effective stress under the condition of K0 consolidation, the coefficient of earth pressure at rest and tangent Poisson's ratio decrease, while the tangent modulus increases. Under the stress paths of K0 consolidation and constant stress ratio, the amount of particle breakage of coral sand within the test stress range is very small and therefore has little effect on the stress-strain curve. Under the constant stress ratio path, the stress-strain curve of coral sand in a certain stress ratio range can be reasonably predicted by the power function model, in which the effects of different constant stress ratio paths on the stress-strain relationship are considered.