In this paper we propose a new generative model for wrinkles on aging human faces using Marked Point Processes (MPP). Wrinkles are considered as stochastic spatial arrangements of sequences of line segments, and detected in an image by proper localization of line segments. The intensity gradients are used to detect more probable locations and a prior probability model is used to constrain properties of line segments. Wrinkles are localized by sampling MPP using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. We also present an evaluation setup to measure the performance of the proposed model. We present results on a variety of images obtained from the Internet to illustrate the performance of the proposed model.