Textile composites have distinct mechanical characteristics different from those of unidirectional composites. Several common weave patterns, 5-harness or 8-harness satin weaves, for example, lack certain symmetry properties common to composites composed of unidirectional layers. The lack of symmetry of woven fabric composites can be drastically reduced, but not totally eliminated, if a laminate consists of one or more flipped pairs, each with one normal layer placed symmetrically about the laminate mid-plane to the flipped layer. To explore more possible combinations in a more general way, a systematic approach is presented by considering a single fabric layer as a sublaminate characterized by a set of stiffness parameters. Mechanical properties of laminates constructed from such sublaminates are obtained by combining the sublaminate stiffness matrices and force and moment resultants. The effects of operations like 908 rotation, flipping, mirroring and their combinations on a sublaminate are discussed. The symmetry properties of weave patterns are classified based on the type of operation necessary for the patterns to be equivalent before and after the operation. The classification of fabric patterns and their coupling coefficients of plate stiffness matrices are found to be dependent on the distribution of crimped regions, or more specifically, the skewness of that distribution. Techniques for achieving symmetry and balance by constructing laminates from flipped and/or rotated pairs are then discussed and found to be, to a certain extent, dependent on the type of equivalence of the weave pattern. It is shown in this study that perfect symmetry cannot be achieved for weave patterns, such as 8-harness satin weaves, with only rotation-flip equivalence. Perfect symmetry and balance can be achieved using as few as four layers, within cell alignment errors, for weave patterns with only mirror-rotation equivalence, like 5-harness satin weaves.