An innovative method for prestressing structural elements through the use of shape memory alloys (SMAs) is gaining increasing attention in research as this method does not require the use of mechanical anchorages for tendons. The activation of the memory effect by means of temperature variations (Joule effect) in effect produces high stresses in SMA components attached to concrete components as reported in the literature. This paper presents the work performed for the purpose of prestressing concrete hollow cylinders with the use of nickel–titanium (Ni–Ti) SMA wires. In the tests, a variety of hollow cylinders were made using the same concrete mix and with the same wall thickness (20 mm), but with different external diameters (200 mm, 250 mm, and 300 mm). Their prestressing was achieved by the means of Ni-Ti SMA wires of different diameters (1 mm, 2 mm, and 3 mm) wrapped around the cylinders. Longitudinal and circumferential strain during the thermal activation of the SMA wires by Joule heating was measured using gauges located on the internal surface of the hollow cylinders. The experimental protocol, recorded observations, and discussion of the effectiveness of the prestressing of concrete elements as a function of the test parameters are included in the text in detail. Comments on the conditions for effective prestressing of concrete cylinders with SMA wires are proposed in the conclusions of the paper.