In the Device-to-Device (D2D) caching network where mobile user terminals are all cache-enabled, the spatial distributions of all users were modeled as the Homogeneous Poisson Point Processes (HPPP). On this basis, combined with the randomness of content caching and requesting, the network interference was analyzed exactly and then approximately under specific scenarios. Considering that the D2D caching technique has the dual characteristics of both caching at terminals and D2D communications, which means that the content offloadeding includes self-offloading way and D2D-offloading way, and the content transmission has to meet the constraints of received Signal-to-Interference Ratio (SIR) and D2D maximal communication distance simultaneously, the closed-form expressions of Successful Offloading Probability (SOP) of the random D2D caching network was deducted. Simulation results show that the proposed SOP is a general metric and can be reduced to the special cases of existing research results. For example, when the users are distributed densely and the D2D maximal communication distance is relatively large, the SOP is reduced to the Successful Transmission Probability (STP) without considering the D2D distance constraint.