The catenary system of a high speed train is designed to have a flexibility to ensure the contact with a pantograph during high speed running. The flexibility inevitably entails a vibration. The vibration is transferred to a utility pole through brackets. Therefore, the examination of the dynamic load at the bracket due to the train running is necessary for the design of the bracket. In this research, an equation of motion is derived to calculate the dynamic load at the bracket during high speed running and a computer program is developed. Also, the analyzed results are compared to characterize the dynamic load at the bracket.