The present study is devoted to developing a yield criterion that can model both the yielding asymmetry and plastic anisotropy of pressure-insensitive metals. First, a new isotropic yield criterion which can model the yielding asymmetry of pressure-insensitive metals is proposed. The main advantage of the proposed criterion is that it leads to a good approximation of yield loci calculated by the Taylor-Bishop-Hill crystal plasticity model. Further, the isotropic criterion is extended to orthotropy to take plastic anisotropy into account. The new anisotropic criterion is general and can be used in three-dimensional stresses. The coefficients of the criterion are determined by an error minimization procedure. Applications of the proposed theory to a hexagonal close packed (HCP) magnesium, a Cu-Al-Be shape memory alloy and a Ni3Al based intermetallic alloy show that the proposed theory can describe well the plastic anisotropy and yielding asymmetry of metals and the transformation onset of the shape memory alloy, showing excellent predictive ability and flexibility.