  The $S=1/2$ Heisenberg antiferromagnet in the ladder geometry is studied as a
model for the spin degrees of freedom of SrCu$_2$O$_3$. The susceptibility and
the spin echo decay rate are calculated using a quantum Monte Carlo technique,
and the spin-lattice relaxation rate is obtained by maximum entropy analytic
continuation of imaginary time correlation functions. All calculated quantities
are in reasonable agreement with experimental results for SrCu$_2$O$_3$ if the
exchange coupling $J \approx 850$K, i.e. significantly smaller than in
high-T$_c$ cuprates.
