Fast neural Electrical Impedance Tomography (EIT) is a method able to image electrical activity in nerves by measuring impedance changes (dZ) which occur as ion channels open. While it can image fast activity in large peripheral nerves, for imaging inside smaller nerves, the signal-to-noise-ratio must be maximized which requires optimization of EIT parameters. If optimized, fast neural EIT could be of benefit in the new field of electrical stimulation of autonomic nerves ("Electroceuticals") that could allow cross-sectional imaging of the fascicles and precise neuromodulation of internal organs supplied by them to treat associated medical conditions. The purpose of this thesis work was to develop an accurate model of nerve fibres that could validate experimental data, predict optimal parameters for imaging with EIT and explain the nature of the observed signals. In chapter 2, relevant literature on EIT, membrane biophysics and existing models of nerve fibres is reviewed. Accurate 3D FEM models of unmyelinated fibres bi-directionally coupled with external space, including Hodgkin-Huxley giant axon of the squid (single and multiple) and mammalian C nociceptor are developed in chapter 3. The models explain available experimental data and optimize fast neural EIT in unmyelinated nerves. In chapter 4, an accurate FEM model of a myelinated fibre coupled with extracellular space is developed and utilized for the same purposes. Dispersion in unmyelinated fibres is studied in chapter 5 by development of the accurate FEM models of 50-fibre HH and C nociceptor nerves, followed by extension to the statistical models of realistic nerves with thousands of fibres. The models provide the maximum distances over which EIT may be used for imaging fascicular activity for each kind of nerve and showed that dZ could be seen further then compound action potential if it is biphasic.