Predicates treated as variables, i. e. parameters, in parallel circumscription make it difficult to compute parallel circumscription. Therefore it is very important to develop powerful methods for eliminating parameters. In this paper, we present some parameter elimination methods in parallel circumscription. At first, we show two fundamental theorems for eliminating parameters. Next, we give two parameter elimlnation methods, which are directly derivable from those theorems. One of them is used for eliminating a parameter which occurs only positively or only negatively in a condition sentence of parallel circumscription. Another is a method for eliminating a parameter by replacing it with a formula expressing the minimal or maximal extension of the parameter. These elimination methods are systematic, and can deal with parameters such that they are quantified with both existential and universal quantifiers in the conditlon sentence. The class of parallel circumscription which can be translated into predicate circumscription by these methods is larger than the one by well known Lifschitz's method.