In this talk, we give a derivative-free method for extreme eigenvalues of even order symmetric tensors, which could be formed as a nonlinear optimization on a unit sphere. Sometimes, derivatives of the objective function may be expensive to evaluate or corrupted by noise. To deal with these difficulties, we propose a derivative-free trust-region algorithm for spherically constrained optimization. Nice geometry of the spherical surface motivates us processing in the tangent bundle, which is a collection of all tangent space of the sphere. At each point on the sphere, the connection between its tangent space and the sphere is explored by the Cayley transform. Using this connection, we construct a quadratic model function by interpolation in the tangent space and produce a trial step by minimizing the model function in a trust region. The next iterate is a point on the sphere corresponding to the trial step if accepted. Under mild assumptions, we prove that the sequence of iterates generated by the proposed algorithm converges to a critical point of the spherically constrained optimization. Preliminary numerical experiments illustrate the promising performances of the new algorithm for spherical optimization without derivatives and extreme eigenvalues of symmetric tensors.