A new theoretical model describing laser hole drilling processes for polymers and fiber reinforced composites has been developed. The model can explain the tapered wall formation and the stabilized hole formation. This model can predict the hole shapes for certain incident beam profiles. We present two specific incident beam shapes, one for a Gaussian incident beam, and the other for an isosceles trapezoid shape beam. For the Gaussian incident beam, we show how the peak fluence, the beam diameter, and the material parameters (absorption coefficient, threshold ablation fluence) affect the hole shapes. For the trapezoid shape beam, we show how the flat top of the beam, the side slope wings, the peak fluence, the threshold fluence and the absorption coefficient affect the hole shapes.