Polymer-based fiber composites have a number of unique physical and mechanical properties and are widely used in the design of structural elements in rocket and space engineering. However, along with the high characteristics of strength and rigidity, there is a noticeable anisotropy of properties which contributes to occurrence and development of damage leading to degradation of the load bearing capacity of structures and their premature destruction. Along with development of micromechanical and phenomenological models, an important place has the procedure for identifying the basic characteristics of composite materials. Such characteristics, in particular, include those of layer elasticity which are usually used when designing structures. However, even such characteristics depend on the loading conditions and for their identification, computational methods based on statistical analysis should be used. This paper attempts to identify the elastic characteristics based on test results of unidirectional carbon plastic with AS4 carbon fibers and polyetheretherketone thermoplastic matrix. For identification, the least squares method was used for samples tested at off-axis angles of 0, 10, 30, 45, 60 and 90 ° and different values of strain rates.