Drawing operations are commonly used to shape metallic thin-walled products for variety of industries – automotive, aerospace, household appliances etc. The basic indicator characterizing cold drawing process is possibility to decrease weight of a product, while at the same time increasing its stiffness in comparison to other conventional manufacturing technologies such as casting, forging or machining. In this research authors presented results of a numerical study on the influence of parameters such as blankholder pressure, forming force, tooling shape and part shape design on the success in manufacturing a part of complicated shape designed as an element of a phase change material heat accumulator. The subject of wrinkling (first and second degree of buckling) was discussed, and the research presented the manufacturing process design which allowed manufacturing discussed drawpiece without defects and within dimensional tolerances. The paper analyzes the phenomenon of drawpiece folding during the forming process for various groups of materials. Experimental research was carried out on a prototype tool for stainless steel (X5CrNi18-10), aluminum alloy (AW-5754) and copper alloy (CW024A).