  We investigate antiferromagnetic spin ladders with nonmagnetic impurities by
variational and numerical (Lanczos and DMRG) methods. The interaction between
the two unpaired spins opposite to the impurities is described by an effective
exchange interaction $J_{eff}$, the magnitude of which depends on the impurity
distance. The magnitude of $J_{eff}$ is different for unpaired spins at the
edges of an open ladder and in the bulk. This difference is related to the
different distribution of the unpaired spin into the bulk of the ladder. The
numerical results are interpreted using matrix product states. Using the DMRG
we calculate the spectrum of low-lying energy levels for up to 6 impurities and
find that these spectra can be reproduced assuming pair interactions with an
accuracy of better than 10\%. We discuss the filling of the ladder gap with
impurity states and argue that in the thermodynamic limit the spin ladder with
a finite concentration of impurities always shows a Curie susceptibility at low
temperatures.
