Formation of the stress-and-strain state of the rock mass in the roof of mined coal seam depends on the development of the mined-out space. It is believed that the coal seam is located deep enough and it can be assumed that the effect of the daylight surface on its condition can be neglected. In this case, the solution is based on the analytical approach using methods of the complex variable theory and it is reduced to the construction of a single permission analytical function. The paper reviews the evolution of the deformation processes in development of the mined-out space in presence of a hard-to-collapse elastic roof, which is capable of sinking smoothly over time, without sudden caving on the landings on the floor. A particular attention is paid to the phase when the roof and the floor touch each other, i.e. the roof caving, starting from the first touching and up to its complete caving. In this case, two sections of the hanging roof are formed, that are gradually reducing in length as the dimensions of the mined-out space increase. The area of roof caving is progressively increasing, and the vertical compressive stresses at the boundary are gradually rising, tending to reach the initial vertical pressure at the depth of the formation before the start of its mining. Tension zones relative to the horizontal and vertical stresses are identified, that are attributed to the areas of roof hang-up, which may determine the location of zones with higher methane and formation water permeability, both in the rocks between the seams and in the coal seam.