In the well logging industry, before designing any kind of logging tools, the tool response needs to be simulated and analyzed in different circumstances. Those kinds of logging tools can be generally categorized into two main genres: frequency domain tools and time domain tools. This dissertation presents a numerical way to simulate the time domain tool response. The 3-D finite difference time method is employed in this dissertation. In this dissertation I used 3D FDTD method to simulate the logging tools response in complicated logging circumstance to see how the response will appear with different formation. A few examples were included in this dissertation and shown very decent results. As it is known that the frequency is set relatively low so the tool can detect further when dealing with well logging problems. In order to improve the efficiency of the entire simulation process, two main techniques are introduced in this dissertation: perfectly matched layer boundary conditions and artificially high dielectric constant. With those techniques combined together, the specific tool (Look-Ahead time do main logging tool) response is studied such as the distance to bed boundary response, sea-bed logging tool response, and reservoir effect. With those cases study in detail, the response patterns are investigated while the formation parameters are varied. One thing that needs to be pointed out is that the source excited in all the examples through this dissertation is a Differential Gaussian wave with different maximum operating frequency chosen based on different needs and different examples. Advisors/Committee Members: Liu, Richard C. (advisor), Vipulanandan, Cumaraswamy (committee member), Wilton, Donald R. (committee member), Charlson, Earl J. (committee member), Malki, Heidar A. (committee member).