The paper deals with optimizing of the headstock of the lathe part of the heavy duty CNC machining centre for 70 ton workpieces using topology optimization. The aim was to find a solution that minimizes compliance and reduces weight of the housing of headstock by 5%. Topology optimization was done in the pre-processor Siemens Simcenter using the NX Nastran solver, which is based on the finite element method. The final structure of topology optimization was used as the concept for the basic layout of the main supporting ribs of the housing of the headstock. The obtained final design provides a high increase of the stiffness of the heavy machining centre in main directions.