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In this paper we considered the most general form of non conformally flatcylindrically symmetric non-static space-times to study proper conformalmotions using direct integration technique. We have shown that very specialclasses for cylindrically symmetric space-times admit proper conformal motions.This classification also covers non-static and static plane symmetricspace-times. In [9] it was claimed that non conformally flat plane symmetricstatic space-times do not admit proper conformal motion. Here it is also shownthat static and non static plane symmetric space-times admit proper conformalmotions. We also discuss the Lie algebra in each case.

Classification of non conformally flat cylindrically symmetric non static space-times according to their proper conformal motions