In this paper, we describe the design of a C library which is named PTPol implementing arithmetic operations for univariate polynomials. We report on practical experiments showing the relevance of using threads on recent multicore computers. We show how to use efficiently an API named OpenMP and POSIX Threads to achieve scalability. On multi-core architectures, we obtain a speed-up equivalent to the number of cores on addition and multiplication on univariate polynomials even for moderate degrees.