Methods of inducing tumor regression, inhibiting tumor growth, and inducing apoptosis with selective peptidomimetic inhibitors of geranylgeranyltransferase I (GGTase I), are provided. In one aspect, GGTI-2418 and its methylester GGTI-2417, increase levels of the cyclin-dependent kinase (Cdk) inhibitor p27Kip1 and induce breast tumor regression in vivo. In another aspect, GGTI-2417 inhibits the Cdk2-mediated phosphorylation of p27Kip1 at Thr187 and accumulates p27Kip1 in the nucleus.