The general solution for squeeze flow between closely-spaced plates of arbitrary shape includes an in-plane potential how whose components satisfy the Cauchy-Riemann conditions, and the velocity held and the pressure are both determined by the boundary conditions at the edge of the plates. In contrast, the velocity field for the infinite-plate limit only requires boundary conditions at the surfaces of the plates. The infinite-plate problem is singular, and makes sense only as a limit of a sequence of hows in finite geometries, each of which has a well-defined coordinate origin. (C)1999 Elsevier Science B.V. All rights reserved.