Radial and elliptic flow in noncentral heavy-ion collisions can constrain t
he effective equation of state (EOS) of the excited nuclear matter To this
end, a model combining relativistic hydrodynamics and a hadronic transport
code [Sorge, Phys. Rev. C 52, 3291 (1995)] is developed. For an EOS with a
first-order phase transition, the model reproduces both the radial and elli
ptic Bow data at the SPS. With the EOS fixed from SPS data, we quantify pre
dictions at RHIC where the quark-gluon plasma (QCP) pressure is expected to
drive additional radial and elliptic flows. Currently, the strong elliptic
flow observed in the first RHIC measurements does not conclusively signal
this nascent QGP pressure.