We present the first evidence of charmless decays of the B(s)(0) meson, the decay B(s)(0)->phi phi, and a measurement of the branching ratio BR(B(s)(0)->phi phi) using 180 pb(-1) of data collected by the CDF II experiment at the Fermilab Tevatron collider. In addition, the BR and direct CP asymmetry for the B(+)->phi K(+) decay are measured. We obtain BR(B(s)(0)->phi phi)=[14(-5)(+6)(stat)+/- 6(syst)]x10(-6), BR(B(+)->phi K(+))=[7.6 +/- 1.3(stat)+/- 0.6(syst)]x10(-6), and A(CP)(B(+)->phi K(+))=-0.07 +/- 0.17(stat)(-0.02)(+0.03)(syst). Both decays are governed in the standard model by second order (penguin) b -> s(s) over bar s amplitudes. RI Lancaster, Mark/C-1693-2008; Ruiz, Alberto/E-4473-2011; Robson, Aidan/G-1087-2011; De Cecco, Sandro/B-1016-2012; Wolter, Marcin/A-7412-2012; St.Denis, Richard/C-8997-2012; Prokoshin, Fedor/E-2795-2012; Chiarelli, Giorgio/E-8953-2012; Azzi, Patrizia/H-5404-2012