We have studied the kinematics of stellar disc populations within the solar neighbourhood in order to find the imprints of the Galactic bar . We carried out the analysis by developing a numerical resolution of the 2D2V ( two-dimensional in the physical space , 2D , and two-dimensional in the velocity motion , 2V ) collisionless Boltzmann equation ( CBE ) and modelling the stellar motions within the plane of the Galaxy within the solar neighbourhood . We recover similar results to those obtained by other authors using N-body simulations , but we are also able to numerically identify faint structures thanks to the cancelling of the Poisson noise . We find that the ratio of the bar pattern speed to the local circular frequency is in the range \Omega _ { B } / \Omega = 1.77 to 1.91 . If the Galactic bar angle orientation is within the range from 24 to 45 degrees , the bar pattern speed is between 46 and 49 km.s ^ { -1 } .kpc ^ { -1 } .