Earth and rockfill dam can be constructed having vertical or inclined core with varying thickness. The thickness of the core for vertical and inclined core depends upon the quantity of fine-grained and course-grained materials available at site. This paper presents analytical study carried out for the thick inclined core to determine the critical thickness of inclined core under end-of-construction condition (EOC). Stability analysis was performed for 180 m high earth and rockfill dam with an upstream slope of 1 in 2.70 and a downstream slope of 1 in 1.90. The clay core with varying upstream inclination is studied along with varying base thickness of the core from 60 to 450 m. Parametric study with respect to relative strength parameters of core to shell and variation of pore water pressure constant (ru) was carried out with varying thickness of inclined core. This paper presents critical thickness of inclined core within which factor of safety (FoS) for upstream and downstream side slopes of the dam would be safe. The critical thickness of core was found to be 275 m. The critical slope has been arrived for both upstream and downstream slope as 1 V: 0.86 H and 1 V: 0.55 H, respectively.