In this paper,we investigate the invariant rings of two classes of finite groups that are generated by a number of generalized transvections with invariant subspaces H over a finite field in the modular care. We name these groups by generalized transvection groups. The one class is concerned with a given invariant subspace which is involved several roots of unity. Constructing quotient group and tensor, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties.The other one is concerned with different invariant subspaces which have same dimension. We Provide a classification of these groups and illustrate their invariant rings in detail.