For S ⊆ G, let κ(S) denote the maximum number r of edge-disjoint trees 4782&_mathId=si1.gif&_user=111111111&_pii=S0096300315014782&_rdoc=1&_issn=00963003&md5=11be656dc2a0b3097ed20b73cc594ac2" title="Click to view the MathML source">T1,T2,…,Tr in G such that 4782&_mathId=si2.gif&_user=111111111&_pii=S0096300315014782&_rdoc=1&_issn=00963003&md5=97099ac10ecfb705f4b180998903982d" title="Click to view the MathML source">V(Ti)∩V(Tj)=S for any 4782&_mathId=si3.gif&_user=111111111&_pii=S0096300315014782&_rdoc=1&_issn=00963003&md5=3a30cbd364cb86730aceae87dc03e4c7" title="Click to view the MathML source">i,j∈{1,2,⋯,r} and i ≠ j. For every 2 ≤ k ≤ n, the generalized k-connectivity of G κk(G) is defined as the minimum κ(S) over all k-subsets S of vertices, i.e., 4782&_mathId=si4.gif&_user=111111111&_pii=S0096300315014782&_rdoc=1&_issn=00963003&md5=7d9586e9814bc64773ae667847c6eaa3" title="Click to view the MathML source">κk(G)= min 4782&_mathId=si5.gif&_user=111111111&_pii=S0096300315014782&_rdoc=1&_issn=00963003&md5=8317c9ee7dd67160b2ee2a0a35ff06aa">4782-si5.gif">. Clearly, κ2(G) corresponds to the traditional connectivity of G. The generalized k-connectivity can serve for measuring the capability of a network G to connect any k vertices in G. Cayley graphs have been used extensively to design interconnection networks. In this paper, we restrict our attention to two classes of Cayley graphs, the star graphs Sn and the bubble-sort graphs Bn, and investigate the generalized 3-connectivity of Sn and Bn. We show that 4782&_mathId=si6.gif&_user=111111111&_pii=S0096300315014782&_rdoc=1&_issn=00963003&md5=6a6ff45dd55448204945ab2844634644" title="Click to view the MathML source">κ3(Sn)=n−2 and 4782&_mathId=si7.gif&_user=111111111&_pii=S0096300315014782&_rdoc=1&_issn=00963003&md5=f0d4f209fc02b22d464d2654f74655b5" title="Click to view the MathML source">κ3(Bn)=n−2.