occurs [3; 5; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. Nevertheless, others indicate that fibers do not contribute to the increase of the strength [24]. In addition, there is research that indicates that improvements may occur up to a certain value of the fiber content [19; 25; 26]. Among the reasons given for this variation in opinions are the effect of fibers on the transversal confinement of the specimens [14; 15], the influence of the so-called fiber factor (product of the volumetric fiber ratio by its fiber aspect ratio, \(\phi_{f}\lambda\)) [27], the sensitivity to the fiber volume-aggregate size relationship, linked to the workability of the material [27], and the creation of additional voids in the concrete matrix [14; 24]. In regard to the elasticity modulus, \(E_{f}\), there also appears a disparity of results. There are works that demonstrate that the addition of steel-fibers tends to reduce it [13; 14; 28; 29; 30], while in others, an increase has been recorded [3; 15; 16; 17; 18]. The reasons for explaining the decrease are associated with the creation of additional voids that involve the inclusion of fibers [28; 29; 30]. With regard to the critical strain at peak load, \(\epsilon_{cf}\), there is a consensus that an increase occurs with the addition of steel-fibers [3; 6; 8; 16; 17; 18; 31; 32; 33; 34], which is associated both with \(\phi_{f}\), as well as \(\lambda\)[14] and with the mentioned fiber factor [18; 29]. The influence that the increase of \(f_{cf}\)[18; 29; 35; 36] has on this parameter is also reported. Once the maximum load is reached is when the principal effect of the steel-fibers is observed on the compression behavior of the concrete in terms of ductility and toughness. In all the works consulted, it is evident that the addition of fiber increases the capacity of energy absorption during the strain of the material, thereby improving its ductility [3; 4; 5; 6; 14; 15; 16; 17; 18; 24; 31; 32; 33; 34; 37; 38; 39]. This is due fundamentally to the greater effect of transversal confinement that fibers provide [5; 6; 14; 15; 18; 24]. On the other hand, the design and analysis of the structural elements made with SFRC requires the application of models that are capable of representing with exactitude their mechanical behavior for purposes of being able to be included in the current design codes and structural requirements. In the scientific literature, there is a variety of models that, as a function of their own experimental data, pursue approaching the stress-strain response of the SFRC in compression [3; 5; 6; 15; 16; 18; 24; 28; 40]. With closer study, it may be verified how each one of them correctly adjusts to the data from which it comes; however, the adjustment is not as strong when they are subjected to the scrutiny of other experimental sources [30]. With this background, it is pertinent to propose a profound analysis for which the principal parameters are related to the concrete and steel-fibers that have an influence on the compression response of the SFRC. In particular, the increase of ductility and the capacity of energy absorption can be studied by means of the work of volumetric strain in the pre- and post-phases to peak load. For this purpose, a database has been created through an extensive bibliographic search in the scientific literature with compression results for SFRC. It includes a total of 197 uniaxial compression tests on cylindrical specimens with dimensions of \(150\times 300\) mm\({}^{2}\) (diameter \(\times\) height) of SFRC with hook ended fibers with a single fold, in addition to their corresponding matrices without reinforcement. Subsequently, applying the response surface methodology [41], a series of factors, associated with the characteristics of the material (concrete matrix and fiber reinforcement), is analyzed, thereby identifying which have a great effect on the different responses of the compression strength for SFRC. Lastly, the compression stress-strain model for SFRC by [PERSON] et al. [42] is studied.