We study comparatively wide class of regular and quasi-regular three-dimensional elastic frameworks of orthogonal structure that are extremely elongated in one direction. We pay main attention to the construction of approximate models for a compound rod with regular structure. We use a rectangular parallelepiped with two diagonal non-interacting rods at each face as a basic structural element. Eliminating some groups of rods from this basic structural element, we can consider various regular and quasi-regular frameworks. Using a complete theory of such frameworks based on equations in partial differences, we arrive at a discrete three-dimensional problem. We construct approximate models for compound rods. These theories may be considered as some kinds of discrete analogues to the Timoshenko and Bernoulli models for continuous rods. The pronounced advantages of the models proposed are that they are based on ordinary finite equations and thus a discrete one-dimensional problem should be analyzed. The effectiveness of the models proposed is illustrated by particular examples.