This paper describes the analyses of the prosody of Vietnamese emotional speech, accomplished to find the relations between prosodic variations and emotional states in Vietnamese speech. These relations were obtained by investigating the variations of prosodic features in Vietnamese emotional speech in comparison with prosodic features of neutral speech. The analyses were performed on a multi-style emotional speech database which consisted of Vietnamese sentences uttered in different styles. Specifically, four emotional styles were considered: happiness, sadness, cold anger, and hot anger. Speech data in the neutral style were also collected, and prosodic differences of each style with respect to this neutral baseline were quantified. The acoustic features related to prosody which were investigated were fundamental frequency, power, and duration. According to the analysis results, for each speaker of the database, a set of prosodic variation coefficients was produced for each emotional style. This will help for bringing emotions into Vietnamese synthesized speech, making them more natural.