Steel multi-wire cables are widely used in civil engineering as load-carrying members. The basic element of these cables is usually a simple straight strand made of a straight core and one layer of helical wires. Several difficulties arise in the understanding of guided ultrasonic waves in such structures, partly due to the helical geometry and the inter-wire coupling effects. In the context of non-destructive evaluation, this work aims at theoretically investigating the propagation of elastic waves in helical waveguides. A numerical method is chosen based on a semi-analytical finite element technique that relies on a specific non-orthogonal curvilinear coordinate system. This system is shown to be translationally invariant along the helix centerline so that a spatial Fourier transform can be explicitly performed along the axis and the problem is reduced to two dimensions. It is shown that the method can be readily used for the analysis of helical structures by considering the special case of no curvature. Results for single straight and helical wires are first computed in order to validate the approach. A dispersion analysis for a seven wire strand with simplified contact conditions is then realized.