ABSTRACT In this paper, we investigate the impact of higher-order distortions on the precise measurement of weak gravitational lensing shear and flexion. We begin by defining$x_\mathrm{ s} = \theta /r_\mathrm{ s}$ generalized higher-order distortions and outlining methods for measuring them. Then, using several lens models, we examine how these distortions affect shear and flexion measurements. Our results show that neglecting higher-order distortions can introduce systematic errors of a few per cent in both shear and flexion measurements, indicating that these effects cannot be ignored. Although the strength of these errors depends on factors such as lensing strength and the size of background sources, we demonstrate that simultaneous measurement of higher-order distortions can reduce the systematic errors to below 1 per cent in most cases. Finally, we also present several investigations of these measurement errors in terms of their physical scales.