There is growing interest in the use of low-cost highly sensitive magnetic field sensors for applications ranging from small memory devices to biomedical applications. Among these sensors, the magneto-impedance (MI) sensor has demonstrated a resolution on the order of 10-9T. The MI effect is a sensitive realignment of a periodic micromagnetization in response to a external magnetic field. To date, their design optimization has involved the use of trial and error methods along with models that decouple the small and large scale equations describing the MI effect. To improve the design optimization process for weak field measurements, this thesis research develops a numerical model for predicting MI responses to weak fields, treating both space and time, relaxing assumptions made formerly. This thesis research is organized into three tasks. We begin with a complete formulation of the equations of motion describing the MI effect, using Maxwell and the Landau-Lifshitz-Gilbert equations along with boundary conditions. Spatial discretization deploys a recently developed tool known as meshless methods that enables efficient optimization of the degrees of freedom. For time discretization, projection methods are used. In this approach, we can characterize the coupling effects of micromagnetic and macro phenomena such as the effects of crystalline anisotropy on the field distributions. We compute solutions for common MI configurations in both strong and weak field regimes. Lastly, validation is done by comparisons to fully linear macro-models, linear decoupled models, and experimental data. The proposed thesis research will contribute to a better understanding of MI sensors, providing higher fidelity predictions for weak field responses, and potentially extend the applications requiring detection of weak magnetic fields. Although this numerical model is developed in the context of an MI sensor, the methods used here can also be extended to other weak field sensors.