The finite element method (FEM) has difficulty solving certain problems where adaptive mesh is needed. Motivated by two engineering problems in live-object handling project, this research focus on a new computational method called the meshless method (MLM). This method is built upon the same theoretical framework as FEM but needs no mesh. Consequently, the computation becomes more stable and the adaptive computational scheme becomes easier to develop. In this research, we investigate practical issues related to the MLM and develop an adaptive algorithm to automatically insert additional nodes and improve computational accuracy. The study has been in the context of the two engineering problems: magnetic field computation and large deformation contact. First, we investigate the effect of two discretization methods (strong-form and weak-form) in MLM for solving linear magnetic field problems. Special techniques for handling the discontinuity boundary condition at material interfaces are proposed in both discretization methods to improve the computational accuracy. Next, we develop an adaptive computational scheme in MLM that is comprised of an error estimation algorithm, a nodal insertion scheme and a numerical integration scheme. As a more general approach, this method can automatically locate the large error region around the material interface and insert nodes accordingly to reduce the error. We further extend the adaptive method to solve nonlinear large deformation contact problems. With the ability to adaptively insert nodes during the computation, the developed method is capable of using fewer nodes for initial computation and thus, effectively improves the computational efficiency. Engineering applications of the developed methods have been demonstrated by two practical engineering problems. In the first problem, the MLM has been utilized to simulate the dynamic response of a non-contact mechanical-magnetic actuator for optimizing the design of the actuator. In the second problem, the contact between the flexible finger and the live poultry product has been analyzed by using MLM. These applications show the developed method can be applied to a broad spectrum of engineering applications where an adaptive mesh is needed.