Engineering polymers generally exhibit asymmetric yield strength in tension and compression due to different arrangements of molecular structures in response to external loadings. For the polymeric materials whose plastic behavior follows the Drucker–Prager yield criterion, the present study proposes a new method to predict both tensile and compressive yield strength utilizing instrumented spherical indentation. Our method is decomposed into two parts based on the depth of indentation, shallow indentation, and deep indentation. The shallow indentation is targeted to study elastic deformation of materials, and is used to estimate Young's modulus and yield strength in compression; the deep indentation is used to achieve full plastic deformation of materials and extract the parameters in Drucker–Prager yield criterion associated with both tensile and compressive yield strength. Extensive numerical computations via finite element method (FEM) are performed to build a dimensionless function that can be employed to describe the quantitative relationship between indentation force-depth curves and material parameters of relevance to yield criterion. A reverse algorithm is developed to determine the material properties and its robustness is verified by performing both numerical and experimental analysis.