The packing of rod-like particles has arisen in a variety of scientific and industrial applications. For the factors that attribute to the packing properties of such particles, elongation effect is one of the most important. However, rodlike particles can be easily assembled into non-convex shapes, in which the effects of non-convex deformations should be concerned. In this paper, the dense random packings of identical intersecting spherocylinders with central symmetry are numerically simulated through an analytical model and the relaxation algorithm. The maximally dense random packing (MDRP) states of 2D and 3D intersecting spherocylinders with various aspect ratios are determined from the order maps. In the MDRP states, the specific volume V, defined as the reciprocal of the packing density do, shows a highly linear correlation with the aspect ratio (w >= 1.0), which is similar to the monophasic packing of spherocylinders. This indicates that the elongation effect is the main shape factor that attributes to the packing density. Consequently, the explicit formulas to predict the packing densities of 2D and 3D intersecting spherocylinders are built as single-variable functions of the aspect ratio. The dense random packing density of 2D intersecting spherocylinders equals to that of identical spherocylinders when w=1.25. This suggests that a balance exists between the relative excluded volume effect and the multi-point contact effect to the packing density of non-convex particles. (C) 2016 Elsevier B.V. All rights reserved.