Abstract: In this paper.from the.fundamental equations of three dimensional elasticmechanics, we have found a sequence of asymptotic solving equations of thick ringshell (or body) applied arbitrary loade by the perturbation method based upon ageometric small parameter a=r₀/R₀, which may be divided into two independentequation groups which are similar to the equation groups for plane strain and torsionalproblems. Using these equations, we have also found first order and second orderapproxiniate solutions of thick ring shell applied moment M₀.

Key words: rotational systems, relativity, analytic mechanics, differential equation, conserved quantity, thick ring shell, perturbation, asymptotic equations, stressanalysis, Lie symmetry