In　elastoplastic　analyses,　a　yield　function　needs　convexities　and　C1　continuities,　to　meet　the　requirement　of　return　mapping　algorithms.　However,　many　classic　criteria　in　geotechnical　engineering　have　shortages:　either　numerical　issues　(nonconvexity　and　gradient　discontinuities)　or　insufficient　physical　properties　(lack　of　tensile　strength　and　compressive　cap).　To　overcome　these　deficiencies,　a　smoothed　classic　(SC)　yield　function　is　proposed　after　combining　the　generalized　classic　yield　function,　a　robust　smoothing　technique,　and　investigations　on　physical　meanings.　It　can　reflect　general　soil　properties,　including　basic　shear　strength,　tensile　strength,　compressive　cap,　and　the　impact　of　intermediate　principal　stress.　The　yield　function　is　convex　and　C2　continuous;　therefore,　it　avoids　many　numerical　issues　in　describing　general　strength　behavior.　In　addition,　it　can　provide　a　close　approximation　to　the　Mohr-Coulomb　criterion　to　avoid　discontinuous　gradients.　Formulas　for　the　gradient,　the　Hessian,　and　the　calibration　procedure　are　provided.　(c)　2021　American　Society　of　Civil　Engineers.