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We examine a few families of semistandard Young tableaux, for which weobserve the cyclic sieving phenomenon under promotion.  The first family we consider consists of stretched hook shapes, where we usethe cocharge generating polynomial as CSP-polynomial.  The second family we consider consists of skew shapes, consisting ofrectangles. Again, the charge generating polynomial together with promotionexhibits the cyclic sieving phenomenon. This generalizes earlier result by B.Rhoades and later B. Fontaine and J. Kamnitzer.  Finally, we consider certain skew ribbons, where promotion behaves in apredictable manner. This result is stated in form of a bicyclic sievingphenomenon.  One of the tools we use is a novel method for computing charge of skewsemistandard tableaux, in the case when every number in the tableau occur withthe same frequency.

Promotion and cyclic sieving on families of SSYT