ABSTRACT Prior to the introduction of steering tools and MWD survey equipment, all deflection tools produced circular arc deflections. In order to drill a circular arc deflection the directional driller must change the tool face angle during the course of the correction. With modern bent housing motors and MWD or steering equipment, it is easier and more precise to make corrections using constant toolface angles. Holding a constant tool-face angle produces a uniform vertical build rate which is especially useful for the horizontal driller. This paper presents the derivation of the trajectory equations for drilling constant toolface deflections. The paper also includes both the equations as well as several forms of graphic solutions.