The Linear Joule Engine Generator (LJEG) incorporates the Joule Engine technology and the permanent magnet linear alternator design, which is a promising power generation device for the applications of range extenders for electric vehicles, Combined Heat and Power (CHP) systems, or as a stand-alone power unit. It combines the advantages from both a Joule Engine and a linear alternator, i.e. high efficiency, compact in size, and flexible to renewable energy integration, etc. In this paper, the background and recent developments of the LJEGs are summarised. A detailed 0-dimentional numerical model is described for the evaluation of the system dynamics and thermodynamic characteristics. Model validation is conducted using the test data obtained from both a reciprocating Joule Engine and a LJEG prototype, which proved to be in good agreement with the simulation results. The fundamental operational characteristics of the system were then explained using the validated numerical model. It was found that the piston displacement profile has certain similarity with a sinusoidal wave function with an amplitude of 51.0 mm and a frequency of 13 Hz. The electric power output from the linear alternator can reach 4.4 kW(e). The engine thermal efficiency can reach above 34%, with an electric generating efficiency of 30%.