Stimulated by the exciting progress in experiments, we carry out a combined analysis of the masses, and strong and radiative decay properties of the B and B s -meson states up to the second orbital excitations. Based on our good descriptions of the mass and decay properties for the low-lying well-established states B 1 (5721), B * 2 (5747), B s1 (5830) and B * s2 (5840), we give our quark model classifications for the high mass resonances observed in recent years. It is found that (i) the B J (5840) resonance may be explained as the low mass mixed state B(|S D L ) via 2 3 S 1 -1 3 D 1 mixing, or interpreted as the 2S -wave state B(2 1 S 0 ). (ii) The B J (5970) resonance may be assigned as the 1 3 D 3 state in the B meson family. (iii) The narrow structure around 6064 MeV observed in the B + K − mass spectrum at LHCb may be mainly caused by the B sJ (6109) resonance decaying into B * + K − , and favors the assignment of the high mass 1D-wave mixed state B s (1D ′2 ) with J P = 2 − . (iv) The relatively broader B sJ (6114) structure observed at LHCb may be explained with the mixed state B s (|S D H ) via 2 3 S 1 -1 3 D 1 mixing. Most of the missing 1P-, 1D-, and 2S -wave B-and B s -meson states have a relatively narrow width, they are most likely to be observed in their dominant decay channels with a larger data sample at LHCb.