Both have been remastered from the original production tapes and contain numerous bonus tracks.
The bonus disc for Run With the Pack has 14 songs, 12 of which were never released.
Burnin' Sky's bonus disc features unreleased versions of nearly every song on the album, including alternative takes and mixes of "Man Needs a Woman" and "Morning Sun," and a full version of "Too Bad." Burnin' Sky celebrated its 40th anniversary last week -- it was released on March 3rd, 1977.
Both albums will be available in numerous configurations, including vinyl and digital, on May 26th.
Bad Company's first two albums -- Bad Company and Straight Shooter -- were reissued in 2015.