A particular aspect in the perception of sound is concerned with what is commonly termed as texture or timbre. From a perceptual perspective, timbre is what allows us to distinguish sounds that have similar pitch and loudness. Indeed most people are able to discern a piano tone from a violin tone or able to distinguish different voices or singers. This thesis deals with timbre modelling. Specifically, the formant theory of timbre is the main theme throughout. This theory states that acoustic musical instrument sounds can be characterised by their formant structures. Following this principle, the central point of our approach is to propose a computer implementation for building musical instrument identification and classification systems. Although the main thrust of this thesis is to propose a coherent and unified approach to the musical instrument identification problem, it is oriented towards the development of algorithms that can be used in Music Information Retrieval (MIR) frameworks. Drawing on research in speech processing, a complete supervised system taking into account both physical and perceptual aspects of timbre is described. The approach is composed of three distinct processing layers. Parametric models that allow us to represent signals through mid-level physical and perceptual representations are considered. Next, the use of the Line Spectrum Frequencies as spectral envelope and formant descriptors is emphasised. Finally, the use of generative and discriminative techniques for building instrument and database models is investigated. Our system is evaluated under realistic recording conditions using databases of isolated notes and melodic phrases.