Some diffusion problems in the impression and diffusional creep of anisotropic materials are analyzed. It is found that at the limit of low stress, both the diffusional creep rate and impression velocity are proportional to the applied stress. For a parallelepiped crystal under simple tension or compression in theZdirection, the diffusional creep rate depends on all three principal diffusivities,DX,DY, andDZ. Two limiting cases depend on the quantity &sqrt;DXDY/DZ. When this quantity is large the creep rate is proportional to &sqrt;DZbut when it is small the creep rate is independent ofDZ. For a cylindrical crystal under tension or compression in the axialZdirection, the creep rate depends onDr/DZ. When the ratio is large, the creep rate is the same as the isotropic case except that the effective diffusivity is &sqrt;DrDZ. When the ratio is small, the creep rate is proportional toDrand independent ofDZ. For the impression creep of a half‐space the punch velocity is proportional to the geometric mean of the principal diffusivities parallel and perpendicular to the loading direction, and inversely proportional to the punch dimension. For impression creep of a thin film deposited on an impermeable substrate under the same punching stress, the impression velocity is dependent only on the diffusivity parallel to the thin film, and inversely proportional to the square of the punch dimension. Without the substrate, the impression velocity is dependent only on the diffusivity perpendicular to the thin film, inversely proportional to the thickness of the film, and independent of the punch dimension. ©1994 American Institute of Physics.