  The effects of non-magnetic impurities randomly doped into a two-leg
Heisenberg spin ladder are investigated. Using the continuous time quantum
Monte Carlo loop algorithm we calculate the uniform and staggered
susceptibilities of such a system. The obtained uniform susceptibility is well
described in terms of an effective model of weakly interacting local moments
induced by non-magnetic impurities for a 1% doping case, but not for higher
concentrations. The staggered susceptibility however is significantly enhanced
over that in the effective model already at 1% doping. Using a mean field
approximation for the interladder coupling, we explain qualitatively the phase
diagram of Sr(Cu_{1-x}Zn_x)_2O_3.
