Since Max Matthews pioneering piece Daisy, singing synthesis has been informed by research in speech synthesis and phonetics. A voice may be modeled as an excitation (the glottis) filtered by a resonant cavity, which can be done by analysing recorded vocal sounds with linear predictive coding and then regenerating the sound with independent control of pitch and timbre.
It is crucial to be able to create the right spectral formants for each vowel, and hopefully also make the transitions between vowels or phonemes sound convincing. There are a few methods of formant synthesis, such as FOF. Diphone synthesis is a method concerned with the transitions between steady state segments. An early method of speech synthesis was to use short fragments of recorded spoken words and automatically fit pieces together into words and sentences. This kind of concatenative synthesis has found renewed interest in the last 15 years with the work of Diemo Schwartz, Bob Sturm and others. By transposing the segments to the required pitches it would be easy to use concatenative synthesis to simulate a singing voice. Johan Sundberg has done extensive research on the singing voice.
For an advanced speech synthesis software, you might have a look at Praat, but be warned that it has a steep learning curve and is not made specifically for musical purposes.