The phenomenon of erossion is known as one of the most important causes of damage to pipelines, which reduces the thickness in different areas. Reduction in thickness causes more stress to be concentrated in the pipelines and failure occurs more easily. Ultrasonic tests are one of the methods used to inspect pipelines. Among the various techniques of this type of test, the Lamb guided waves have a special place due to the low depreciation in the propagation path; But the complex behavior of these waves in structures of variable thickness makes it difficult to interpret the data obtained from a test. It is so difficult to study the behavior of Lamb waves in pipes with variation in thickness. Therefore, in this paper, two-dimensional modeling of the finite elements of the behavior of these waves and the study of transmission and reflection coefficients in the presence of thickness variations have been investigated. The results of the study of the effect of changing the erossion depth on the transmiting and reflecting signals indicate that using the Lamb waves test, changes in the thickness of a piece can be well monitored. Also, the study of changes in the frequency of the signal sent to the plate shows that in some frequency ranges, the S0 mode created to deal with the defect has very little sensitivity to changes in thickness. Therefore, choosing the appropriate frequency in inspections performed by Lamb waves is an important step in determining the condition of the structure.