The theoretical model, treating increasing of elastic modulus of fibers from carbon nanotubes at introduction of transverse π-π-bridging between separate nanotubes in fiber. It has been shown that on elastic modulus of fiber three factors influenced, namely, elastic modulus of starting nanotubes, level of interactions between separate nanotubes in fiber and its aspect ratio, i.e. the ratio of fiber length to its diameter. In transition point of the indicated interactions from repulsion to attraction the elastic modulus of fiber achieves the value of corresponding parameter individual carbon nanotube and in region of attractive interactions exceeds it. The structure of fibers, characterized by their fractal dimension, is basic factor for stiffness of fibers of carbon nanotubes. Keywords: fiber, carbon nanotubes, π-π-bridging, nanotubes interactions, structure, elastic modulus, fractal dimension.