Two-dimensional surface-plasmon polariton waves, which propagate at a metal/dielectric interface, exhibit unique and attractive properties. These extraordinary properties, however, are accompanied by fundamentally inherent losses. The latter is probably the most pronounced challenge in the field of plasmonics and a true bottleneck for many applications. Shape-preserving beams, on the other hand, are unique solutions of the wave equation; they maintain their shape with propagation and also possess the ability to self-reconstruct. Here, we study the first realization of surface-plasmon shape-preserving beams, which maintain their shape and intensity over long distances, even when subjected to plasmonic losses. Moreover, their intensity distribution along propagation can be arbitrarily tailored. This is achieved without the use of any gain media, but rather by strictly controlling the initial plasmonic wavefront. This approach can be valuable for a variety of plasmonic applications, such as surface particle trapping and manipulation, on-chip communication, nonlinear optics, and more.