Abstract: Behavior of phase singularities in the distorted optical field is studied by numerical modeling using four-dimension code when a laser beam propagates through uplink and downlink atmospheric turbulence paths. The results reveal that, when the laser beam propagates along an uplink turbulent atmosphere path, the density of phase singularities (DPS) starts at zero and then grows rapidly with the increasing of the propagating height. When the beam propagates to a certain height, the DPS reaches its maximum and then begins to decrease. Such a height changes with the turbulence strength. The stronger the turbulence strength, the bigger the generated DPS, and the lager the maximum DPS with correspondingly lower height. When the laser beam propagates along a downlink turbulent atmosphere path, the stronger turbulence strength is taken, the phase singularities emerge at a higher altitude and the DPS in distorted optical field is bigger near the ground. The functional form of the DPS has a shape of monotone increase with the decrease of the propagation height and the DPS reaches its maximum near the ground. In addition, formulas describing the relationship between the DPS and propagation height/distance are found out. When the laser beam propagates through turbulent atmosphere along an uplink path, the formula is very similar to the formula used for describing the Blackbody radiation in physics. When the laser beam propagates along a downlink atmospheric turbulence path, the DPS seems to be growing exponentially with the propagating distance.