This paper implements algebraic elimination methods for an accurate and general calibration of parallel robots, applied to Gough (or Stewart) platforms. It focuses on two approaches, namely algebraic variable elimination and monomial lineariza- tion, which are compared to a classical numerical optimization technique. We detail the former, since it is not often used for the problems at hand, and specify its application by means of the sparse resultant, combined with numerical linear algebra. We per- form several experiments that allow us to compare the three meth- ods in the presence of measurement errors. Our main conclusion is that elimination methods offer an interesting alternative to more well-established methods for parallel robot calibration by satisfy- ing the goals of accuracy and robustness. Moreover, out methods require no initial estimate and no hypothesis on the noise distribu- tion in order to derive a quality index per solution.