In the present paper is presented a theoretical research about the lifetime determination of pneumohydraulics accumulators under fatigue conditions. Spherical accumulators were analyzed because, as is known, they have indisputable advantages towards the cylindrical accumulators. The analysis presented is based on the methods of fracture mechanics of materials, considering that in the material structure were detected cracks with different shapes and sizes. The proposed method is illustrated with an example of calculation applied to a spherical shape accumulator.