Estimation of the height of caved and fractured zones above a longwall panel along with the stability conditions of the goaf area are very crucial to determine the abutment stresses, ground subsidence, and face support as well as designing the surrounding gates and intervening pillars. In this work, the height of caving-fracturing zone above the mined panel is considered as the height of destressed zone (HDZ). The long-term estimation of this height plays a key role in the accurate determination of maximum ground surface subsidence and the amount of transferred loads towards the neighbouring solid sections. This paper presents a new stability analysis model of caved material system in the goaf area. For this aim, a theoretical energy-based model of HDZ determination in long-term condition is developed. Then the stability condition of the caved material system is investigated using the principle of minimum potential energy. On the basis of the actual data gathered from the literature, the unstable time period of the caved material system is also calculated. Moreover, the effects of time- and temperature-related parameters and constant coefficients as well as their inherent relations with HDZ are evaluated. Furthermore, sensitivity analysis shows that the two temperature-related constants material constant and time are the most effective variables in HDZ, and the slope of material hardening is the least effective one. The estimated HDZ and the stability time of the caved materials can be successfully applied to determine the induced stress and the maximum surface subsidence, respectively, due to longwall mining.