This paper discusses a new method for measuring and calculating the angle of inclination of a railway support or a contact network support, using an unmanned aerial vehicle flying along a straight path, parallel to the railway track. A review of existing measurement methods is carried out, their advantages and disadvantages are indicated. In the method under consideration, it is proposed to measure angles and distances with six laser scanning rangefinders installed in threes on horizontal and inclined planes on an unmanned aerial vehicle. This allows you to increase the speed and accuracy of determining the angle of inclination of vertical supports. The calculations use the minimum distances from the laser scanning range finder to the top and bottom of the support surface. The formulas use geometric relationships and the cosine theorem to calculate the roll of supports taking into account their taper. Measuring distances and angles three times allows for averaging over them, which significantly increases the accuracy of calculations. A model experiment is carried out on a model of a reinforced concrete contact network support in four orientations. A comparison is made between theoretically calculated and experimentally measured distances and inclination angles. The accuracy of parameter determination complies with regulatory requirements.