Static packings of circulo-polygons and ellipses in two spatial dimensions are systemically studied to determine which shapes can form packings with fewer contacts than degrees of freedom(hypostatic packings),and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from naive constraint counting.We show that the packing density and the average contact number at jamming onset obey a master-like curve for all of the nonspherical particle packings we studied when plotted versus the particle asphericity A,which is proportional to the ratio of the squared perimeter to the area of the particle.Further,the eigenvalue spectra of the dynamical matrix for packings of different particle shapes collapse when plotted at the same A.It suggests that the parameter asphericity can serve as a common descriptor of the structural and mechanical properties of packings of nonspherical particles.For hypostatic packings of nonspherical particles,we verify that the potential energy increases as the fourth power of the perturbation amplitude along modes int the lowest nonzero energy branch,and the number of "quartic" modes matches the number of missing contacts relative to the isostatic value.It implies that certain types of contacts can constrain multiple degrees of freedom and allow hypostatic packings of nonspherical particles to be mechanically stable.In addition,we propose a hypostatic conjecture giving criteria that particle shapes must satisfy to form hypostatic jammed packings.