Resonance is a critical phenomena in the designing of any structure. Piping structure, which is one of the several elements of air conditioning and refrigeration system, undergo severe vibration. In practice different approaches such as experimental, analytical, numerical and statistical methods are used to study vibration characteristics of a structure. Statistical method acts as a first hand tool to judge the behaviour of a system. Statistical methods minimise redesign process and expensive methods of controlling vibrations, saving significant amount of effort, cost and time. In the present study, statistical methods are used to estimate fundamental natural frequency of a pipe by selecting different geometrical parameters. The natural frequency obtained can be used to check resonance. Geometrical parameters, which significantly affect the natural frequency, are estimated by using Design of Experiments (DOE) and Analysis of Variance (ANOVA) techniques. A linear equation that predicts fundamental frequency is formulated using regression analysis. Frequencies predicted by regression model are compared to frequencies obtained from ANSYS Mechanical©. A good correlation is found with error less than 5%.