We propose here, a comprehensive model for the solid-state polymerization (SSP) of a low to moderate molecular weight (MW) prepolymer of lactic acid, to produce high MW poly(L-lactic acid) (PLLA). The reactions are rationally assumed to occur only in the amorphous region, and effective concentrations of end groups, vary with crystalinity, X(c), during SSP. We estimate byproduct diffusivities, D, using free volume theory. The effects of various parameters on the SSP of PLLA prepolymer have been examined with respect to the optimum MW, X(c) and D. We introduce self-consistently, scaling factors of similar to 0.27, in the experimental procedure, to determine via (19)F-NMR, concentrations of the end groups, after converting them to fluorinated ester groups. The relevant reaction rate constants are obtained by fitting to early time data from representative SSP experiments at 150 degrees C, under high vacuum, on PLLA prepolymer powder (i.e., spherical geometry) of number average MW, (M(n0)) over bar similar to 10,200 Da, which attains (M(n)) over bar similar to 150,000 Da, via SSP. The subsequent successful comparison of the model predictions with experimental data throughout the entire SSP duration indicates that the model is comprehensive and accounts for all the relevant phenomena occurring during the SSP to synthesize high MW PLLA. (C) 2011 Wiley Periodicals, Inc. J Appl Polym Sci 122:2966-2980, 2011