We report photoabsorption measurements from the 4p inner shell of singly ionized strontium in the spectral region between 26.0 and 37.4 eV. More than 60 levels of Sr II are reported which are interpreted as singly excited inner-shell transitions 4p(6)5s (2)S(1/2)-> 4p(4)5s((1)P,(3)P)ns, md and doubly excited transitions 4p(6)5s (2)S(1/2)-> 4p(5)4d((1)P,(3)P,(3)D)nl. Multiconfiguration Hartree-Fock calculations are performed in jj coupling and the levels are arranged into Rydberg series converging on seven limits, allowing the identification of two levels in Sr III.