Abstract: The method of mining flat-dipping and sloping beds of a mineral with hydraulic excavation which includes dividing the bed being mined into levels and sublevels. The height of the sublevels is determined by the rock geology of the bed formation. The sublevels, in their turn, are subdivided into blocks, the width of each block being short of the limit length of the steady or self-supporting outreach of the cantilever of the rock of the main roof with the given pattern of cutting into the bed with the cutting drifts and holes defining the short working faces. The spacing of the blocks being worked in the upper and lower sublevels in the direction of strata is set to preclude inter-influence of the bearing rock pressure in the blocks where the stoping work is being done. The method enables the conduction of a stable excavation of the mineral over an extended front of stoping.