We report the conditions (plasma parameters) under which the Rayleigh-Taylor Instability (RTI) develops in an Al plasma produced by a Nd:Yag pulsed laser with a fluence range of 1 to 4 J/cm2, wavelength of 1064nm and 10Hz repetition rate. The used data correspond to different pressure values of the ambient N atmosphere. From previous works, we took the RTI growth rate form as From the perturbation theory the instability amplitude is proportional to e−ηt. Using the drag model, we calculated the plume dynamics equations integrating the instability term and plotted the instability growth profile with the delay time values to get critical numbers for it, in order to show under which conditions the RTI appears.