Amongst the nonlinear generalization of Maxwell electrodynamics, the so-called BI type NLED, whose first nonlinear correction is quadratic function of Maxwell invariant, is completely special.
In this paper, we investigate the horizonless magnetic strings in the presence of two kinds of the BI type NLED [88, 89].
In this work, we take into account the recently proposed BI type models of NLED [88, 89].
At the first step, we introduced a class of static magnetic string solutions in Einstein gravity in the presence of negative cosmological constant with two types of NLED. In order to have real solutions, we obtained a lower limit for the radial coordinate, [rho].