We investigate the unsteady creep unidirectional composite square structure with the elastic fibers of the square cross-section. The problem of determining the properties of composite components on the set of his properties in transverse shear. A structural model of the composite, in which the minimum representative cell consists of four elements. It is assumed uniformity and one-component of the stress-strain state elements. We obtain two groups of basic and allowing transient creep equations: static and kinematic agreed. For each of them in an elastic state formulas for the transverse shear composite modules. Formulated initial task for the theoretical curves of the composite creep. In describing the creep matrix stationary solutions are obtained by law Norton – the formula for the second stage of the creep of the composite as a Norton law. Numerical studies and comparing the results obtained with the known, which showed the effectiveness of the developed models and solutions. These formulas and equations can be useful in engineering practice for the elastic properties of the forecast and the creep of the composite transverse shear.