Classical anisotropic scattering in the laboratory is examined for a moving-target medium. Legendre expansions of the scattering probability function f(v’,v) are given in the physical region for the general case of anisotropic elastic scattering in the center-of-mass system, and the low-order expansion coefficients are listed. The effects of a moving medium are also studied in the angle transformation from center-of-mass to laboratory system, and kinematical constraints linking angles, masses, and particle and material speeds are listed.