The paper attempts to estimate the incubation time of a cavity in the interface between a power law creep particle and an elastic matrix subjected to a uniaxial stress. Since the power law creep particle is time dependent, the stresses in the interface relax. Through previous stress analysis related to the present physical model, the relaxation time is defined by ${alpha}$2 which satisfies the equation $Gamma$0 ｜1+${alpha}$2k｜m=1-${alpha}$2 [19]. $Gamma$0=2(1/√3)1+m($sigma$$infty$/2${mu}$)m($sigma$0/$sigma$$infty$tm) where $sigma$$infty$ is an applied stress, ${mu}$ is a shear modulus of a matrix, $sigma$$infty$ is a material constant of a power law particle, $sigma$=$sigma$0 $varepsilon$ and t elapsed time. the volume free energy associated with Helmholtz free energy includes strain energies associated with Helmholtz free energy includes strain energies caused by applied stress anddislocations piled up in interface (DPI). The energy due to DPI is found by modifying the results of Dundurs and Mura[20]. The volume free energies caused by both applied stress and DPI are a function of the cavity size(${gamma}$) and elapsed time(t) and arise from stress relaxation in the interface. Critical radius ${gamma}$ and incubation time t to maximize Helmholtz free energy is found in present analysis. Also, kinetics of cavity fourmation are investigated using the results obtained by Riede[16]. The incubation time is defied in the analysis as the time required to satisfy both the thermodynamic and kinetic conditions. Through the analysis it is found that [1] strain energy caused by the applied stress does not contribute significantly to the thermodynamic and kinetic conditions of a cavity formation, 2) in order to satisfy both thermodynamic and kinetic conditions, critical radius ${gamma}$ decreases or holds constant with increase of time until the kinetic condition(eq.40) is satisfied. Therefore the cavity may not grow right after it is formed, as postulated by Harris[11], and Ishida and Mclean[12], 3) the effects of strain rate exponent (m), material constant $sigma$0, volume fraction of the particle to matrix(f) and particle size on the incubation time are estimated using material constants of the copper as matrix.