In recent years, mathematical modelling allied to computer simulation has emerged as en effective and invaluable design tool for industry and a discipline in its own right. This has been reflected in the popularity of the growing number of courses and conferences devoted to the area. The North East Polytechnics Mathematical Modelling and Computer Simulation Group has a balanced representation of academics and industrialists and, as a Group, has the objective of promoting a continuing partnership between the Polytechnics in the North East and local industry. Prior to the present conference the Group has organised eight conferences with a variety of themes related to mathematical modelling and computer simulation. The theme chosen for the Polymodel 9 Conference held in Newcastle upon Tyne in May 1986 was Industrial Vibration Modelling, which is particularly approp riate for 'Industry Year' and is an area which continues to present industry and academics with new and challenging problems. The aim of the Conference was to calIon and use the modelling experience of eminent academics and industrialists who are deeply involved in the solution of vibration problems. To this end the following four sessions were organised: (1) Vehicular Vibrations led by keynote speaker Dr S King (Westland Helicopters Ltd) (2) Acoustics led by Dr M Petyt (Southampton University) (3) Fluid/Structural Vibrations led by G T Willshare (British Maritime Technology) (4) Special Problems and Developing Areas to include nonlinearities, ultrasonics, transients, elastic stability, etc.