An investigation pertaining to estimation of the elastic generalized coordinates for a given class of flexible structures is presented. To begin with, a model for studying nonlinear dynamics of the structure is described. The governing equations of motion are obtained using the Lagrangian procedure with modal discretization. Next, deformations caused by rapid slewing maneuvers are estimated using the least square estimation approach. As an alternative, a procedure based on the operator spline technique is proposed and its potential assessed. It is motivated by the need for achieving an on-line estimation procedure permitting real time control. Finally, a comparative performance study of the two procedures is undertaken using a simplified model of the flexible system.