The Don Cossacks surged into the Neil Simon Theater on Tuesday night for a two-week run with music and dance guaranteed to charm the most jaded of audiences. The performing lies somewhere between the simplicity and straightforwardness of the Red Army Chorus and the sophisticated professionalism of the Moiseyev Dance Company. The scenes of village life are not so very different from the usual folk-troupe fare, though the strong, massed Cossack voices and the rhythmic weave of some of the stamping footwork are special. What reaches so directly across the footlights is the warmth and humor of the performers, particularly the men.
In its first American tour since 1976, the company is offering a beautifully costumed, nicely varied program of song and dance. It is said that the volatile and ebullient Cossacks - ''adventurous'' or ''free'' men in Russian - along the Don River have an exceptional affinity for music, with Cossack singers making up a large part of many Russian choirs. And the dances flowed naturally from the music. It is possible to see the vigor of Cossack horsemen -in some ways the equivalent of American frontiersmen of the 19th century - in the men's gliding runs across the stage and in their pall-mall acrobatics. It is almost impossible, staid urbanite though one might be, to sit still while the lilting, rollicking instrumental music and song flow from the stage.
The first sight of the musicians, singers and dancers, gradually filling the stage in a signature folklore epic called ''Bylina,'' set the mood for the evening. The women are dressed in brocade, velvet and gold and jewels, but the cut and the soft, vibrant colors of the dresses and headpieces make them believable as country folk. And the men are dashing yet staunch in their tunics, flowing pants and boots, all topped off by mustaches that they frequently tweak and curl with panache.
There is the stirring sight of the male choir, voices weaving in plaintive harmony, hushed then swelling as the men cluster on a dark stage, as if around a campfire, for the haunting traditional ''Cossack's Lament.'' ''Horsemen and Friends'' is one of those numbers that almost forces one to dance into the aisles. And '' 'Twixt Forest and Mountain,'' a traditional song sung a cappella by the female choir, was a virtuosic highlight that drew cheers from the audience.
Performing on native instruments, the musicians not only accompanied the singers and dancers but also had a moment or two of their own center stage. One of the evening's most telling moments occurred during ''Fantasy on Themes of Don Folk Songs,'' a duet performed by Aleksandr Mischenko on the balalaika and Andrei Golsky on the bayan, with the kind of silent, intense communication of jazz musicians. The audience started to clap along in one lilting segment. Mr. Mischenko looked out, quieting the clappers with a quizzically stern look. We are artists, his look seemed to say, and worthy of complete attention. And indeed they were.
The fast-stepping dances, performed in long garlanding ranks and in high-kicking, gliding couples, are interesting too for their anecdotal humor. In the delicious ''When Cossacks Cry,'' choreographed by V. Kopylov to music by Boris Ogurtsov, a group of hard-working women rebel against their lazy men - who are good for nothing, it seems, but singing - and trade places with them.
In ''Grandfathers,'' choreographed by G. Galperin to music by Mr. Ogurtsov, a trio of geezers stagger and lurch themselves into a frenzy when a pretty woman walks into their midst. It was performed to the hilt by Mikhail Tabunkin, Pavel Grigoriev, Vyacheslav Pashkov and Lyudmila Glukhova. The ''Don Festival Suite'' is a finale that packs in a bit of all the best of the evening, including some charming high jinks for tall and short male dancers, two of whom are superb comedians. It is a finale that is, like the program itself, both vibrant and compellingly sweet-natured.