Mutants of Ras are oncogenic drivers of a large number of human tumors. Despite being recognized as an attractive target for the treatment of cancer, the high affinity for its substrate tagged the protein as undruggable for a few years. The identification of cryptic pockets on the protein surface gave the opportunity to identify molecules capable of acting as allosteric modulators. Several molecules were disclosed in recent years, with sotorasib and adagrasib already approved for clinical use. The present study makes use of computational methods to characterize eight prospective allosteric pockets (P1-P8) in K-Ras, four of which (P1-P4) were previously characterized in the literature. The present study also describes the results of a virtual screening study focused on the discovery of hit compounds, binders of the P4 site that can be considered as peptidomimetics of a fragment of the SOS αI helix, a guanine exchange factor of Ras. After a detailed description of the computational procedure followed, we disclose five hit compounds, prospective binders of the P4 allosteric site that exhibit an inhibitory capability higher than 30% in a cell proliferation assay at 50 μM.