Analyses of variable flow rate tests have been given special attention recently because it is generally impractical to keep a constant flow rate long enough in the field to perform a drawdown test. Also, in many other situations, the early time data are usually affected by wellbore storage. For fractured wells, this early time period represents linear or bilinear flow in fractures. Thus, it is very important to devise a technique that would allow a petroleum engineer to obtain reservoir in addition to fracture characteristics such as fracture conductivity and fracture half-length, using this early flow data. In this paper, a new mathematical model is developed to describe drawdown and buildup tests for wells intersected by finite conductivity fractures. This new model utilizes the convolution method to arrive at a solution for downhole pressure versus time using simultaneously measured downhole pressure and sandface rates. Analysis based on the solution of this new model allows one to calculate directly both reservoir and fracture characteristics. Results obtained are verified by solving two field examples to demonstrate the model capabilities. A step by step procedure for analysis is also presented.