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As a new technique for structural dynamic analysis, local structural modification is playing a more and more important role in solving practical engineering problems. This thesis develops methods for vibration reduction via local structural modification. In this thesis, the reduction of unwanted vibration in a structural system is principally analysed in two ways, (i) relocation of resonance, and (ii) relocation of anti-resonance - both of which are realised by using local structural modification techniques. The local structural modification is characterised by locally varying the physical parameters of the structural system, and, an algorithm is developed for the finite element implementation. The algorithm which determines the physical parameters to achieve the desired resonances and anti-resonances can be obtained by solving a non-linear polynomial eigen-problem. Examples illustrating the use of various finite element models along with a practical structure are provided to verify the algorithms developed in this thesis and to illustrate the potential of the methods for solving vibration reduction problems in complicated engineering structural systems. In addition, a procedure for structural dynamic optimisation is developed to eliminate the unwanted resonance peak from frequency response functions using the 'POLE-ZERO' cancellation principle via local structural modification. This procedure enables the structural system to preserve certain dynamic properties after structural modification. Numerical and experimental simulations are presented to illustrate the general procedure and to demonstrate the capability of the method.