The presented data cover experimental and numerical axial load-shortening results of steel tubes infilled with rubberised alkali-activated concrete. The experimental data are obtained from 36 concrete filled steel tube specimens with circular and square cross-sections, length-to-diameter/width ratios of 2 and 4, and three different rubber contents in the concrete infill. The data from the numerical assessment cover the axial load-shortening response of over 300 finite element models. These cover a wide range of concrete infill strengths and rubber contents, steel tube grades, specimen widths, and steel tube wall thicknesses. Detailed descriptions of the material and methods, experimental testing, and numerical modelling procedures are also provided. The data reported herein supports the discussion in the research article "Axial compressive behaviour of composite steel elements incorporating rubberised alkali-activated concrete," and in the case of the numerical parametric assessment, give for the first time the full axial load-shortening response of all the models considered.