  We study a model of the stripe state in strongly correlated systems
consisting of an array of antiferromagnetic spin ladders, each with $n_{leg}$
legs, coupled to each other through the spin-exchange interaction to charged
stripes in between each pair of ladders. The charged stripes are assumed to be
Luttinger liquids in a spin-gap regime (Luther-Emery). An effective interaction
for a pair of neighboring ladders is calculated by integrating out the gapped
spin degree of freedom in the charged stripe. The low energy effective theory
of each ladder is the usual nonlinear $\sigma$-model with additional cross
couplings of neighboring ladders. These interactions are found to favor either
in-phase or anti-phase short range spin orderings depending on whether the
charge stripe is site-centered or bond-centered as well as on its filling
factor and other physical parameters of the charged stripe.
