We report STAR results on the azimuthal anisotropy parameter v(2) for strange particles K(0)(S), Lambda, and Lambda at midrapidity in Au+Au collisions at sqrt[s(NN)]=130 GeV at the Relativistic Heavy Ion Collider. The value of v(2) as a function of transverse momentum, p(t), of the produced particle and collision centrality is presented for both particles up to p(t) approximately 3.0 GeV/c. A strong p(t) dependence in v(2) is observed up to 2.0 GeV/c. The v(2) measurement is compared with hydrodynamic model calculations. The physics implications of the p(t) integrated v(2) magnitude as a function of particle mass are also discussed.