A spherocylinder, a convex 3D object consisting of a cylinder with two hemispherical ends, can possess a wide range of aspect ratios and is one of the most studied non-spherical particle shapes. Previous investigations on disordered spherocylinder packings yielded inconsistent packing characteristics, especially the packing density φ, indicating that density alone is not sufficient to uniquely characterize a packing. In this paper, we delineate in the density–order–metric diagram (i.e. order map) the border curve that separates geometrically feasible and infeasible packings of congruent spherocylinders via the geometric-structure approach, i.e., by generating and analyzing a large number of packing configurations with a diversity of densities and degrees of order generated via a relaxation algorithm. We find that the border curve possesses a sharp transition as the packing density increases, i.e., the initial increase of φ is not associated with any notable increase of the degree of order, while beyond a threshold φ value, the increase of density is strongly positively correlated with the increase of order. This allows us to propose the concept of maximally dense random packing (MDRP) state for spherocylinders, which corresponds to the transition point in the boarder curve and characterizes the on-set of nontrivial spatial correlations among the particles. It can also be considered as the maximally dense packing arrangement of spherocylinders without nontrivial spatial correlations. The degree of order of a spherocylinder packing is quantified via the nematic order parameter (S) and the local order metric (SLocal), which respectively characterize the level of global orientational order and local order in particle clusters. The latter metric SLocal, which measures the average order in the neighborhoods of particles with the second Legendre polynomial, is a new order metric for spherocylinder systems. We find that the packing density of the MDRPs initially increases with the increase of the aspect ratio w from 0, and reaches the maximal value of 0.725 when w=0.5, then drops with further increase of w. The MDRP at w=0.5 is verified to be jammed via a Monte Carlo jamming-testing algorithm and thus, should also represent the maximally random jammed (MRJ) packing state as well. Display omitted •The local order in clusters is identified as a main order form in geometric spherocylinder packing.•A new local order metric SLocal is proposed to quantify the local order in clusters.•The concept of maximally dense random packing (MDRP) state in spherocylinder packings is proposed.•In the MDRP state, the packing properties in terms of the aspect ratio are presented.