In general formant frequencies are most significant parameters required for synthesis of speech sounds particularly vowels. The present study was conducted to estimate the first four formant frequencies of the (Hindi) Vowel sound and to synthesize vowel sounds based on the computed values. The minimum and maximum values of formants for accurate perception of these sounds were also determined. The speech samples consists of ten Hindi vowels spoken in a fixed context by a male speaker. These samples were digitized using a 12 bit A/D converter and a LSI-11/23 C.P.U. based mini-computer system. In order to reduce the computation, the end points of the utterence was detected by an end point algorithms which is based on energy calculation and zero crossing rate. The digitized signal was pre-emphasized for high frequency components. A 256 point Hamming Window was applied to emphasize the zero-frequency region of the spectrum. For the estimation of formant frequencies the capstraly smoothed log-spectra is used. The peaks of this spectra corresponding to formant frequencies were computed for all the vowels under study.