The saturable absorption of Yb3+/Na+ codoped CaF2 crystals at 1050nm has been demonstrated by comparative experiments by inserting the novel Yb3+,Na+:CaF2 crystal with different doping concentrations into a Yb:YAG laser in stable continuous wave operation, which is the cause for the crystals working as the gain material to tend to self-Q-switching at 1050nm. The results show that the dominative element is Yb3+ rather than Na+ for saturable absorption action of the crystals. However, the effect of Q-switching by codoping Na+ into the CaF2 crystals can be greatly improved so that the Yb3+,Na+:CaF2 crystals with optimum concentration and doping ratio can be used as a Q-switching element at 1050nm.