Brad's musical roots started at an early age. At home both of his parents were avid music fans and musicians themselves. Brad's earliest memories are of his dad picking out Luther Perkin's guitar parts off of Johnny Cash's albums. He'd sit on the arm of the couch and play his Fender Mustang through a Fender Twin Reverb Amp. Brad's mom, an accomplished vocalist and pianist had picked up the classical guitar when Brad was about 12 years old. When the guitar didn't work out for her she gave it to Brad and he started taking private lessons. Having three years of piano lessons under his belt already he soon excelled at the guitar and the bond had begun. By the age of 18 Brad had enrolled in the University of North Texas' music program to study classical guitar and voice. He had developed a close relationship with singer/lyricist Eddie Allen and within two years of entering college they had both dropped out in order to pursue music full time. The two continued to write and perform together for five years. They were well recieved at clubs such as The Hop in Fort Worth, Poor David's Pub in Dallas, Kerrville Folk Festival and other venues that were havens for budding young songwriters. In '92 the partnership ended and Brad began a solo career.

Brad Thompson & The Undulating Band was formed later that year as a vehicle for Brad's original music that he had been writing since his split with Eddie. His songwriting and performing soon began showing the influences of solo guitarists such as Michael Hedges and rock bands such as Toad the Wet Sprocket and Counting Crows. He patterned the formation of the band after artists such as Lyle Lovett and Jeff Buckley who put their music in the capable hands of the finest musicians and the end result - great music regardless of what style or category with which you try to define it. When asked about the bizarre/lengthy name for his band, Brad recalls a radio interview he heard long ago with original Van Halen lead singer, David Lee Roth, just before taking the stage in front of thousands of fans at the famous US Festival in California in 1983. In Roth's typical pre-show banter he says something about "Giving the crowd their fifty bucks-worth tonight on a silver platter man..." then he pauses and says "...and it'll be undulating." You could hear the interviewer and everyone backstage just fall about the place laughing it was so hilarious. Brad says, "As campy and ridiculous as Roth was, he was very serious about entertaining people. I had to use that word undulating, plus it adds balance to an otherwise ordinary sounding name."