Vibration is a response from a mechanical system that occurs due to the excitation force given.Vibration on the Main Engine foundation is very influential on the construction. As in ro-ro ships thatexperience changes to the main engine, which in the end also requires the addition of plates on the mainengine foundation to fulfill the alignment value between the main engine and the gearbox. This FinalProject discusses the vibrations that occur in the ship's main engine foundation using mathematicalmodeling methods. Mathematical modeling is used to determine the system that works in a mathematicalstatement. Preliminary analysis conducted to determine the value of mathematical modeling. Thedeflection and stiffness values also affect the vibration response that occurs in the main enginefoundation. This mathematical modeling produces a vibration response in the form of a vibrationresponse equation and the resulting equation can produce a graph by entering the equation into theMatlab software. The vibration response graph uses two variations, namely at 85% RPM and 100% RPM.From the calculation results obtained amplitude values of 0.179 mm at 85% RPM and 0.199 mm at 100%RPM before adding the plate. And has an amplitude value of 0.172 mm at 85% RPM and 0.191 mm at100% RPM after adding the plate. According to the ABS the recommended displacement is below 1.0 mmand the probability of damage is above 2.0 mm. This shows that the vibrations that occur in this structureare permitted.