Anisotropic flow of Ks, K̅s and Λs is studied in heavy-ion collisions at SPS and RHIC energies within the microscopic quark–gluon string model. At SPS energy the directed flow of kaons differs considerably at midrapidity from that of antikaons, while at RHIC energy kaon and antikaon flows coincide. The change is attributed to the formation of dense meson-dominated matter at RHIC, where the differences in interaction cross-sections of hadrons become unimportant. The directed flows of strange particles, v₁^K,K̅,Λ (y), have universal negative slope at |y| ≤ 2 at RHIC. The elliptic flow of strange hadrons is developed at midrapidity at times 3 ≤ t ≤ 10 fm/c. It increases almost linearly with rising p_t and stops rising at p_t ≥ 1.5 GeV/c reaching the same saturation value v₂^K,Λ(p_t) ≈ 10 in accord with experimental results.