Side-pumped Nd:YAG lasers of 86 W quasi-fundamental mode diode-lasers is presented. In experiment, the Nd:YAG crystal with the dimensions of is side-pumped by diode-lasers from three directions. Convex mirrors are used to increase mode volume with a 90° rotator to compensate thermal depolarization. Right parameters of cavity are acquired by experiments and stimulations. At last, the maximum output power of 86 W is achieved with M2<2. The changes of beam width of radia l and tangential polarization with the length of thermal lens are stimulated. Parameters of the laser are numerical calculated, which are in good agreement with the experimental results. right expanding and focusing system are designed, and the relationship between the laser beam waist position and input current is acquired.