The paper reports an initial study on computational poetry generation for Bengali. Bengali is a morpho-syntactically rich language and partially phonemic. The poetry generation task has been defined as a follow-up rhythmic sequence generation based on user input. The design process involves rhythm understanding from the given input and follow-up rhyme generation by leveraging syllable/phonetic mapping and natural language generation techniques. A syllabification engine based on grapheme-to-phoneme mapping has been developed in order to understand the given input rhyme. A Support Vector Machine-based classifier then predicts the follow-up syllable/phonetic pattern for the generation and candidate words are chosen automatically, based on the syllable pattern. The final rhythmic poetical follow-up sentence is generated through n-gram matching with weight-based aggregation. The quality of the automatically generated rhymes has been evaluated according to three criteria: poeticness, grammaticality, and meaningfulness.