  We study a massive cosmic strings with BII symmetries cosmological models in
two contexts. The first of them is the standard one with a barotropic equation
of state. In the second one we explore the possibility of taking into account
variable \textquotedblleft constants\textquotedblright ($G$ and $\Lambda
).$Both models are studied under the self-similar hypothesis. We put special
emphasis in calculating the numerical values for the equations of state. We
find that for $\omega\in(0,1]$, $G$, is a growing time function while
$\Lambda$, behaves as positive decreasing time function. If $\omega=0,$ both
\textquotedblleft constants\textquotedblright, $G$ and $\Lambda,$ behave as
true constants.
