In general, identification of structural parameters may be categorized as inverse vibration problem. Usual method of identification uses the values of the parameters initially given to the structure by an engineer. It then modifies the original parameter values as per the observed values from test by an iteration process. The parameters involved in the said problems are traditionally considered as crisp. But, rather than crisp value we may have only the uncertain or incomplete information about the parameters being a result of errors in observations etc. These uncertainties may be modeled through probabilistic, interval or fuzzy theory. Unfortunately, probabilistic methods may not able to deliver reliable results with required precision without sufficient data. Hence interval and fuzzy theory are becoming powerful tools for handling the uncertainties in recent decades. This paper investigates the identification procedures of the uncertain column stiffness of multistorey frame structures by using prior known estimates of the uncertain parameters and uncertain dynamic data. Uncertainties are modeled through triangular convex normalized fuzzy sets. Bounds of the uncertain parameters are obtained by using a proposed fuzzy based iteration algorithm. Example problems are solved to demonstrate the reliability and accuracy of the identification process.