A new point of view on the calculation of the exact spectrum of two dimensional sigma models in finite volume is presented. We will start from the bootstrap S-matrix, asymptotic Bethe ansatz equations, pass through the construction of bound states and Y-system (TBA), and finally use the integrable T-system (Hirota equation) to end up with convenient Destri-de-Vega-like integral equations to solve the problem numerically. The approach will be demonstrated on the $O(4)$-sigma model.