We report results of a study of charmless B meson decays to three-body Kππ, KKπ and KKK final states. Measurements of branching fractions for B decays to K=+(0)π+π-, K +K+K-, K0K+K-, K+Ks 0Ks 0 and K s 0Ks 0Ks 0 final states are presented. The decays B0→K0K +K-, B+→K+Ks 0Ks 0 and B0→Ks 0Ks 0Ks 0 are observed for the first time. We also report evidence for B+→K +K-π+ decay. For the three-body final states K0K+π-, Ks 0K s 0π+, K+K+π - and K-π+π+, 90% confidence level upper limits are reported. Finally, we discuss the possibility of using the three-body B0→Ks 0K+K - decay for CP violation studies. The results are obtained with a 78 fb-1 data sample collected at the Y(4S) resonance by the Belle detector operating at the KEKB asymmetric energy e+e- collider. © 2004 The American Physical Society.