This Graduation Thesis deals with the design of steel structures for the verification of serviceability limit states as imposed by Eurocode standards. Firstly, the general definitions of ultimate and serviceability limit states are shown, which are defined in the basic Eurocode standard. Next, the implementation of the global analysis of steel structures is presented. The main part lists serviceability design criteria for steel structures which are obtained from the Slovenian National Annex to standard EN 1990 and criteria from AISC Design Guide. Numerical example demonstrates the design of steel frame and steel purlin, where different design approaches are adopted. Design using the plastic and elastic global analysis considering the second order theory is presented. The appropriate verifications of the limit states are demonstrated following the selected design approach.