The finite difference time domain method is employed to calculate the radar signatures of an obliquely penetrating tunnel in various background media. The relatively faster propagation of electromagnetic signal and stronger distortion in the first peak were discovered due to the existence of an empty tunnel as its penetration angle becomes more oblique. It renders the arrival time of the first peak to be increased relatively slower than that of the first received signal. To analyze the different behaviors of two arrival times, those data are compared with the straight line model and the ray-tracing model. Finally, the relation between the penetration angle of an empty tunnel and the arrival time of received pulse signatures is evaluated with the curve fitting model in three different background media. These results are compared with the measured data in a well suited tunnel test site.