In this paper, we study the map projections from pseudo-sphere $S_1^2$ onto the non-lightlike surfaces in the 3-dimensional Lorentzian space, $L^3$, with curvature zero. We show geometrical means and properties of $mathbb{R}{ imes}S_1^1-cylindrical$, $S^1{ imes}L-cylindrical$ and $mathbb{R}{ imes}H_0^1-cylindrical$ projections defined on $S_1^2$ to cylinders $mathbb{R}{ imes}S_1^1,;S^1{ imes}L$ and $mathbb{R}{ imes}H_0^1$, respectively, and orthographic and stereographic projections on $S_1^2$ to Lorentzian plane, $L^2$.