This thesis is concerned with the free vibration analysis of stiffened circular cylindrical and conical shells. The study was carried out with a view to improving the accuracy and efficieny of various modelling techniques for the prediction of the stiffened shells natural frequencies and mode shapes. A review of the existing literature covering various aspects of the shell vibrations problem and modelling techniques has been given at the beginning of each chapter with a critical appraisal of the assumptions made and results obtained. Initially the continuum energy approach was used for the analysis. The developed method allows for discrete consideration of stiffeners having arbitrary location and properties. Energy of bending in two planes and rotary inertia have been included in the analysis. Various types of stiffened shells with shear diaphragm ends condition were analysed using this method for the prediction of their natural frequencies. The predicted results have been compared with published experimental results. The finite element technique was also used for the prediction of natural frequencies and mode shapes of stiffened shells. Axisymmetric shell of revolution element, Facet shell element, semi-100f element and various types of beam elements, which are available within the PAFEC 75 suite of programs, were used for these studies. An efficient modelling technique has been introduced for ring stiffened cylindrical and conical shells by the use of the shell of revolution element. For improved accuracy of the predicted frequencies and a more economical model, shell symmetry was utilized for the free vibration analysis of unstiffened and stiffened shells. Half, quarter and one eighth models were studied by developing the appropriate boundary conditions and are discussed here. The free vibration characteristics of orthogonally stiffened cylindrical shells and an orthogonally stiffened cylindrical panel have been studied. An eight noded stiffened super shell element was developed for this study. This element was used for modelling various other types of stiffened shells and the predicted natural frequencies have been compared with known published experimental and theoretical results. Experimental verification of theoretical predictions of natural frequencies and mode shapes of an orthogonally stiffened cylindrical panel was carried out and is reported here.