The failure probability and the reliability index have been determined for a pipe submitted to internal pressure, exhibiting a corrosion defect, embedded in a soil with a ground reaction, and underwent the displacement due to seismic activity. Results are obtained by computing the condition of failure: strain demand higher than strain resistance which is typically the Strain Based Design (SBD) basis. From the probabilistic point of view, this condition results in the overlay of the two probability distributions, namely, demand and resistance. An analytical method is proposed to compute the common area between the strain demand and resistance distribution and then to get the probability of failure. The strain demand is assumed to follow a power-law distribution and the strain resistance is a Normal one. The strain demand is computed assuming that the probability density of seismic waves follows a Gutenberg - Richter distribution law. This simple method is also used to predict the failure probability of different reference periods or seismic zone. It is also used to examine the influence of the coefficient of variation of the strain resistance distribution when using vintage pipe steels.