A new method is introduced by using the cross-spectral density function to describe the caustics beam, which is extended from fully coherent cases to the field of partially coherent cases for the first time. And the propagation formula of caustics beam is derived in the free space combined with the Fresnel Kirchhoff diffraction integral theroy. The influence of astigmatism introduced by tilted axicon at various inclination angles on partially coherent caustic beam with respect to the propagation axis was studied theoretically and experimentally. Furthermore, the partially coherent caustics beam is invested that is effected by the field coherence on the partially coherent caustic beam. Results show that the intensity contrast ratio between light focus and the surrounding dark regions can be reduced with the decrease of the spatial coherent lengths.