High-temperature Co-electrolysis of H2O and CO2 in a solid-oxide electrolyser (Co-SOE) for syngas production is a high-efficiency renewable electricity conversion and storage method part of the Power-to-X technologies. Syngas, a mixture of H2, CO and CO2, is a critical building block to make several chemical and synthesis fuels. The thesis aimed to model the Co-electrolysis process in a steady-state process modelling tool called Aspen Plus. The model was designed at thermoneutral mode and four cases with electrolysis temperatures of 700 °C, 750 °C, 800 °C and 850°C. The results from the model were used to perform an economic assessment and check the feasibility of Co-SOE. The analysis included calculation of Net Present Value (NPV), Internal Rate of Return (IRR) and the Levelised cost of Syngas (LCOS). The LCOS from Co-SOE was compared to the benchmark technology of syngas production in a Reverse Water Gas Shift (RWGS) reactor. The H2 feed to the RWGS reactor was assumed to be obtained from a Proton Exchange Membrane Electrolyser(PEME). A sensitivity analysis was performed to check the effect of electricity price, electrolyser stack price, electrolyser lifetime, CO2 feed price, by-product O2 revenue and discount rate on the LCOS. The LCOS was calculated to be 0.697, 0.727, 0.752 and 0.783 €/kg at 700 °C, 750 °C, 800 °C and 850 °C, respectively, increased with temperature due to increased electricity consumption at thermoneutral mode. The average LCOS from Co-SOE was 18.5% cheaper than the benchmark technology due to the high investment in the PEME and low conversion efficiency of the RWGS process. There was a trade-off between LCOS and system efficiency due to the effect of internal methanation occurring on the cathode side of the SOE. 750 °C was found to be the optimum design temperature to minimise the LCOS and maximise the efficiency. LCOS was most sensitive to electricity price, followed by O2 revenue and discount rate, while other parameters were less significant. The thesis also discussed key challenges to overcome in the future development of the Co-SOE technology. Co-SOE was found to be a promising technology for green syngas production. However, challenges concerning low stack lifetime, high capital investment and high cost of electricity have yet to be overcome to demonstrate it at a commercial scale.