For the advantages of environment-friendly decomposition product, fireproofing, and low cost, the water or water-based dielectric is widely used in die-sinking electrical discharge machining (EDM) and wire EDM, especially in the high-efficiency electrical erosion process. In order to study the process of EDM in water, in this paper, a theoretical spark column expansion formula has been derived instead of directly using the previous empirical expressions for EDM in oil dielectric. It is found that the approximate expression of the proposed formula is extremely close to the previously widely used empirical expression for EDM in oil dielectric when the parameters are selected appropriately. The corresponding parameters for EDM in water are determined according to the dimensions of experimentally obtained craters. The proposed theoretical formula reveals that the total heat transfer time decreases radially from the center to the periphery at the spark/anode interface rather than equals to the pulse on time everywhere. This phenomenon can be considered as the time integration effect (TIE) caused by the expanding spark, and it has been calculated quantitatively based on the derived formula. Finally, a finite element thermal model considering the TIE has been developed. The results of craters and material removal rate (MRR) predicted by the proposed model show a close agreement with experimental results, which indicates that the developed thermal model can be used to study the spark expansion rule and understand the EDM process. Keywords Electrical discharge machining (EDM) . Spark expansion formula . Finite element thermal model . Time integration effect (TIE) Nomenclature C Combined coefficient (μm 2 /J) C p Average specific heat (J/kg/K) K Average thermal conductivity (W/m/K) i Peak current (A) u Discharge maintaining voltage (V) t e Pulse on time (μs) t off Pulse off time (μs) t h Total heat transfer time (μs) R s Spark column radius (μm) lDistance of discharge gap (μm) r i Initial spark radius (μm) R c Crater radius (μm) h c Crater depth (μm) V c Volume removed per spark (mm 3 ) F a Fraction of energy going to anode T m Melting Temperature (K) T b Boiling Temperature (K) L m Latent heat of melting (kJ/kg) L v Latent heat of vaporization (kJ/kg) T Temperature (K) q 0 Uniform heat flux (W/m 2 ) ρAverage material density (kg/m 3 )