We present a systematic method of evaluating the packing entropy for a
set of mutually avoiding extended, hard, rigid objects on a lattice.
The method generalizes a simple algebraic representation of the lattic
e cluster theory developed by Freed and co-workers for systems compose
d of flexible objects. The theory provides a power series expansion in
z-1 for the corrections to the zeroth order mean field approximation
partition function, where z is the lattice coordination number. We ill
ustrate the general theory by calculating the packing entropy of four-
unit rigid ''square'' objects on a hypercubic lattice as a function of
the volume fraction of the squares. As a particular limiting case, we
also evaluate for the packing entropy of two, three, and four squares
on a two-dimensional square lattice and find agreement with the clust
er expansion.