A search for charmless three-body decays of B-0 and B-s(0) mesons with a K-S(0) meson in the final state is performed using the pp collision data, corresponding to an integrated luminosity of 1.0 fb(-1), collected at a centre-of-mass energy of 7 TeV recorded by the LHCb experiment. Branching fractions of the B-(s)(0) -> K(S)(0)h(+)h'(-) decay modes (h(()'()) = pi, K), relative to the well measured B-0 -> K-S(0)pi(+)pi(-) decay, are obtained. First observation of the decay modes B-s(0) -> (KSK +/-)-K-0 pi(-/+) and B-s(0) -> K-S(0)pi(+)pi(-) and confirmation of the decay B-0 -> (KSK +/-)-K-0 pi(-/+) are reported. The following relative branching fraction measurements or limits are obtained B(B-0 -> (KSK +/-)-K-0 pi(-/+))/B(B-0 -> K-S(0)pi(+)pi(-)) = 0.128 +/- 0.017 (stat.) +/- 0.009 (syst.), B(B-0 -> (KSK+K-)-K-0)/B(B-0 -> K-S(0)pi(+)pi(-)) = 0.385 +/- 0.031 (stat.) +/- 0.023 (syst.), B(B-s(0) -> K-S(0)pi(+)pi(-))/B(B-0 -> K-S(0)pi(+)pi(-)) = 0.29 +/- 0.06 (stat.) +/- 0.03 (syst.) +/- 0.02 (f(s)/f(d)), B(B-s(0) -> (KSK +/-)-K-0 pi(-/+))/B(B-0 -> K-S(0)pi(+)pi(-)) = 1.48 +/- 0.12 (stat.) +/- 0.08 (syst.) +/- 0.12 (f(s)/f(d)), B(B-s(0) -> (KSK+K-)-K-0)/B(B-0 -> K-S(0)pi(+)pi(-)) is an element of [0.004; 0.068] at 90% CL.