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The experimental nominal strength varies with specimen size. Such a phenomenon was investigated earlier by Griffith and Weibull. Recently, several models have been proposed to predict strength reduction with size increase in concrete structures. Confirmation was given of the proposed size effect laws, based on the extensive experimental data that can be found in the literature. Direct tension, splitting, bending, shear and torsion tests have been mainly considered. In particular, direct tension and bending have been recently analysed by Carpinteri et al. On the other hand, the compressive behaviour of concrete, being very complex, has been disregarded. In this paper, which can be considered as the continuation of the two previous ones published in this journal, where the multifractal scaling law was used to explain the scale effects on flexural and tensile strength, scale effects on the compressive strength of concrete specimens are analysed. The failure mode of compressed concrete specimens can be considered as resulting from local tensile mechanisms, or from a combination of tensile and shear mechanisms, according to the specimen geometry. It is thus possible to interpret some experimental investigations reported in the literature through the multifractal scaling law as well as the Bazant’s size effect law, where a tensile failure mechanism is assumed. A comparison between the two best-fit methods is presented. From the interpretation of the experimental results, a criterion to determine the specimen dimension minimizing the size effects is also proposed.

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