The reduction of semiconductor device size to the submicrometer range leads to unique electrical and thermal phenomena. The Fourier conduction effect was not enough to explain the phenomena and we need to bring in nonFourier conduction effects to analyse microelectronic devices. A two-phase lag model is used here to bring in the nonFourier effects. A numerical solution procedure based on the finite element method and fourth order Runge-Kutta time marching procedure has been employed for the spatial and temporal discretisations respectively. The predicted results for different boundary conditions clearly capture thermal wave-like and pure diffusion type phenomena in the appropriate range of time lag values. In electronic packaging, the microscale heat conduction must be considered in view of higher heat fluxes encountered recently, especially when we deal with transient heat transfer. A two dimensional case is considered as a first step. The results are encouraging. © 2000 IEEE.