Either measured displacements or calculated displacements are required in the available implicit algorithms. Two new formulations of the implicit algorithms will be presented herein. Neither measured displacements nor calculated displacements are used in the new algorithms. Hence, propagation errors can be significantly reduced in performing pseudodynamic tests. A series of simulations have been performed to study the error propagation characteristics of the algorithms. For the sake of comparisons, the error propagation characteristics of the implicit algorithm originally proposed by Thewalt and Mahin and that suggested by Shing and Manivanna are also considered in this study.