For the better use of metamaterials, the surface waves of metamaterials are studied in half-space model with dipole radiation source. Using the Sommerfeld integrals of TM wave and TE wave, the branch-cut’s effect on the computation of the integrals is investigated based on saddle point algorithm. The distribution and validity of pole points for the integrands is analyzed according to the properties of complex integral. For TM wave, there are lateral wave and Zenneck surface wave in the case of taking left-handed material as substrate; for TE wave, no Zenneck surface wave can exist in any case of metamaterials.[JP]