A theoretical model for a multicascade liner system is proposed with a view to reduce the growth rate of Rayleigh-Taylor (R-T) instability and to calculate the fusion parameters of a dense θ-pinch plasma. The dynamics of such plasma has been described using the modified snow-plow model for sinusoidal and t1/3 types of discharge current profiles. Numerical results demonstrate that the thermonuclear fusion parameters can be achieved for a dense θ-pinch deuterium-tritium (D-T) fiber plasma for an optimum choice of shell thickness. The relevance of this kind of study is possible use of gas-liner and staged pinches as an alternative source of thermonuclear fusion.