This paper broadens previous research concerning spalling damage in concrete structures under buried explosions, by additionally examining the effects of shell thickness and shell head length of the warhead experimentally and numerically. In the experiment, concrete targets were subjected to the embedded explosion of cylindrical shelled explosives with different charge masses, shell thicknesses, and shell head lengths. The results reveal that thicker charge shells and longer shell heads decrease the surface area and the depth of spalling damage on the rear surface of concrete structures. In addition, to investigate the damage mechanism and predict the critical collapse thickness (CCT), two- and three-dimensional finite-element models were developed and correlated well with the experimental results. Parametric analyses are also applied to examine how the embedded depth, length-to-diameter ratio, shell thickness, and shell head length affect the CCT for a buried explosion. Finally, an empirical formula is proposed to estimate the CCT based on these factors.