Systems of parallel beams connected with springs appear often in engineering. Typical examples are bundles of wires, such as the ones appearing in suspension bridge cables. These connections result in coupling of the differential equations describing the problem. In this paper, two systems of parallel beams connected with springs perpendicular to the beams are examined: multiple beams connected with springs, and multiple beams of common stiffness connected with springs and subjected to a common tensile axial load. A method is proposed to decouple the system of coupled equations into uncoupled differential equations for which exact shape functions can be constructed, so that the computational effort associated with systems involving a very large number of beams can become manageable. Numerical examples are presented demonstrating the capabilities of the proposed method.