A key challenge in further improving infrared (IR) sensor capabilities is the development of efficient data pre-processing algorithms. This paper addresses this challenge by providing a mathematical model and synthetic data generation framework for an uncooled IR sensor. The developed model is capable of generating synthetic data for the design of data pre-processing algorithms of uncooled IR sensors. The mathematical model accounts for the physical characteristics of the focal plane array, bolometer readout, optics and the environment. The framework permits the sensor simulation with a range of sensor configurations, pixel defectiveness, non-uniformity and noise parameters.