We present a theory for probe-induced flow distortion which is applicable in the atmosphere at heights greater than about 10 times the obstacle size. We use the theory to calculate the behavior of Reynolds shear stress and velocity variances ahead of a cylinder and a sphere. The stress is found to be most seriously distorted, the extent depending on the nature of the trailing wake. We show that the linear form of the theory should be adequate for most surface-layer applications, and we discuss how the theory can be applied to more complex geometries. We show that the “tilt correction” approach to the problem, which has been used by some workers, is incorrect in principle since it violates vorticity conservation, and is not even a good approximation in general. Abstract We present a theory for probe-induced flow distortion which is applicable in the atmosphere at heights greater than about 10 times the obstacle size. We use the theory to calculate the behavior of Reynolds shear stress and velocity variances ahead of a cylinder and a sphere. The stress is found to be most seriously distorted, the extent depending on the nature of the trailing wake. We show that the linear form of the theory should be adequate for most surface-layer applications, and we discuss how the theory can be applied to more complex geometries. We show that the “tilt correction” approach to the problem, which has been used by some workers, is incorrect in principle since it violates vorticity conservation, and is not even a good approximation in general.