The stress analysis of Kollar and Springer (1992) Int. J. Solids Structures 29, 1499-1517, is applied to fiber-reinforced organic matrix composite cylinders subjected to hygrothermal and mechanical loads. The wall of the cylinder may be "thin" or "thick". An individual fiber must remain at the same radial distance from the axis; no other restrictions are placed either on fiber orientations or on stacking sequence. The applied loads may vary radially and circumferentially, but not axially. Solutions are presented which yield radially and circumferentially varying strains and stresses inside composite cylinders.