This paper presents a vocal timbre analysis method based on topic modeling using latent Dirichlet allocation (LDA). Although many works have focused on analyzing characteristics of singing voices, none have dealt with "latent" characteristics (topics) of vocal timbre, which are shared by multiple singing voices. In the work described in this paper, we first automatically extracted vocal timbre features from polyphonic musical audio signals including vocal sounds. The extracted features were used as observed data, and mixing weights of multiple topics were estimated by LDA. Finally, the semantics of each topic were visualized by using a word-cloud-based approach. Experimental results for a singer identification task using 36 songs sung by 12 singers showed that our method achieved a mean reciprocal rank of 0.86. We also proposed a method for estimating cross-gender vocal timbre similarity by generating pitch-shifted (frequency-warped) signals of every singing voice. Experimental results for a cross-gender singer retrieval task showed that our method discovered interesting similar pitch-shifted singers.