The kinetics of growth of lamellar crystals by chain folding of polymer molecules are described by Markov rate processes whose states are representations of the edge of a lamella. The dynamic reversibility of these processes allows their equilibrium distributions to be found and these describe states of steady crystal growth. For a hexagonal crystal structure the equilibrium distribution is the Gibbs distribution for a constrained, one-dimensional Ising antiferromagnet. For a square crystal structure it is a constrained exponential distribution. These distributions provide a description of the roughness of the edge of a growing crystal and expressions for the growth rate. The continuum limit of these models is shown to coincide with the model of Frank and of Bennett et al. (J. statist. Phys. 24, 419 (1981)). Frank's approximate equations (Frank, F. C. J. Cryst. Growth 22, 233 (1974)) are also examined.