It is well known that nowadays a significant part of the total energy consumption is related to buildings, so research for improving building energy efficiency is very important. This paper presents our investigations about the dimensioning of horizontal overhangs in order to determine the minimum annual consumption of building primary energy for heating, cooling and lighting. In this investigation, embodied energy for horizontal roof overhangs was taken into account. The annual simulation was carried out for a residential building located in the city of Belgrade (Serbia). Horizontal overhangs (roof and balcony) are positioned to provide shading of all exterior of the building. The building is simulated in the EnergyPlus software environment. The optimization of the overhang size was performed by using the Hooke Jeeves algorithm and plug-in GenOpt program. The objective function minimizes the annual consumption of primary energy for heating, cooling and lighting of the building and energy spent to build overhangs. The simulation results show that the building with optimally sized roof and balcony overhangs consumed 7.12% lessprimary energy for heating, cooling and lighting, compared to the house without overhangs. A 44.15% reduction in cooling energy consumption is also achieved.