Turbines are hydraulic machines which convert hydraulic energy into mechanical energy. This mechanical energy is used in running an electric generator that is directly coupled to the shaft of a turbine. These machines convert mechanical energy into electrical energy. The generation of hydro-electric power is the cheapest as compared to the power generated by other sources such as oil, coal, etc. Power generated by Small Hydro Power (SHP) station is not only cheap, but also environment friendly. Despite its dual advantage, the SHP has however remained untapped all over the world. Things are now changing surely but slowly, with more and more focus on SHP. Hydropower being the cleanest source of electrical energy from environmental considerations needs to be tapped as early as possible. The authors of this paper are motivated by the water current available in the river Brahmaputra, Assam, which may be suitable for establishing Small Hydro Power stations. A design of a prototype of a straight bladed vertical axis water turbine which is based on the theories of vertical axis wind turbine is proposed here. Encouraged by the existing theories of vertical axis wind turbine, the authors propose a mathematical analysis and design of a prototype of vertical axis water turbine which may be suitable for Small Hydro Power Station. Future scope of this work is also mentioned.