Recent experimental results demonstrated that well formed plasma jets can be produced at laser interaction with targets made of materials with high atomic number (A ≥ 29 where A = 29 corresponds to Cu). On the contrary, it is impossible to launch a plasma jet on low-A material targets like plastic. This paper is aimed at explanation of this difference by considering mechanisms responsible for plasma jet formation, i.e., the radiative cooling of ablative plasma and the influence of target irradiation annular profile speculated hitherto, newly complemented by different expansion regimes of the Cu and plastic plasmas (provided by numerical simulations). The experiment was carried out with the PALS iodine laser. Two different planar massive targets, plastic and Cu, as well as the plastic target covered by thin Cu layers of various thicknesses were irradiated by the third harmonic laser beam of energy of 30 J, pulse duration of 250 ps (full width at half maximum), and the focal spot radius of 400 µm. To find the most suitable range of these layers (from 28 to 190 nm) a simple analytical model of laser-driven evaporation was developed. Three-frame laser interferometer and an X-ray streak camera were used as two main diagnostic tools. Numerical modeling was performed with the use of two-dimensional hydrodynamic code ATLANT-HE. Results provided from experiments and theoretical analyses have proved that the process of plasma jet formation is rather complex. Relative importance of the three mechanisms mentioned above depends on the target irradiation geometry as well as the target material used.