The Zhaman-Aibat cupriferous sandstone deposit is developed by the Zhomart Mine which reserves are nearly depleted. The paper suggests the method and the results of the research of natural stress field at the Zhomart mine. Stress measurements were carried out by fissure relief in the walls of single development openings located outside the extraction influence area. Evaluation of the rock stressed-deformed state was performed by mathematical simulation in accord with in-situ measurements made. Data input for the calculations performed included strength and deformation characteristics of gray sand following the laboratory uniaxial tension tests of the core samples retained from the exploratory sites. The field studies and numerical simulation established that the maximum horizontal stresses in the investigated area of the virgin rock at the Zhomart mine reach 27.7 MPa and are directed perpendicularly to the ore-body strike. Accordingly, the minimal main horizontal stresses of 16.2 MPa trend along the ore-body strike. Vertical stresses generated by the rock weight above make up 17.5 MPa. The research results are meant to adjust parameters of the mining system implemented in some tracts under development at the Zhaman-Aibat deposit.