Electrical capacitance tomography (ECT) is a low cost and fast imaging technique able to obtain cross sectional images of dielectric permittivity distribution. ECT has been successfully used in industrial process tomography mainly for 2D imaging. One of the key challenges in 3D ECT imaging is a large scale forward problem arising with a large number of elements in the meshed ECT sensor model. Notably a complete sensor model will provide the most appropriate solution to the forward problem. A complete sensor model requires modelling a shielded area behind electrodes, which leads to increase in density of the finite element mesh. In this thesis, an approximation error model (AEM) has been applied to the ECT modelling for the first time. In addition to 3D AEM modelling and to further evaluate the effectiveness of the proposed AEM algorithm, it was implemented to compensate for uncertainty in electrode size and mesh density in 2D ECT. The results achieved using AEM are promising. In terms of application area, this thesis focuses on fundamental development for possible use of ECT in non-destructive evaluation (NDE) application. In more traditional industrial process application the object is surrounded by a number of electrodes on its boundary. In NDE applications a planar array ECT and volumetric imaging is needed. This thesis presents a 3D planar array ECT sensor using a 3D reconstruction algorithm. The results are validated with a number of experimental tests. 3D planar array ECT imaging was further extended to image both dielectric and metallic samples. To quantify the limitations of planar array ECT, a 3D ECT sensor and 3D ECT software have been implemented and used to evaluate the performance of the 3D ECT imaging with missing sides, with planar array ECT being the most extreme case of missing sides. The underlying inverse problem was analysed using singular value decomposition of the sensitivity matrix for the first time. This thesis introduces the use of a resolution matrix to analyse the performance of a 3D ECT reconstruction algorithm. These analysis methods, which enabled an in depth analysis of imaging performance with missing sides, are able to quantify the performance of planar array ECT.