Polyacetylene, as the simplest and the most typical conjugated polymer system with great potentials in electronics industry, was intensively studied both experimentally and theoretically in the recent decades. Many important issues about polyacetylene have been made clear, but there are still some important questions to be answered by further study. Quantum chemists often choose to extrapolate the oligomer properties to obtain the polymer properties, while the solid state physicists prefer to start with periodic boundary condition. In this article, the geometry, electronic structure and polarizability and the second hyper-polarizability of trans polyacetylene chain were studied with first principles calculations. Several commonly used functionals and basis sets were used in the study. Comparing with experimental results, the chemical model CAMB3LYP with 6-311G(d,p) basis set presents a good description for geometry, electronic structure and polarizabilities of trans polyacetylene. Response of trans polyacetylene to a longitudinal electrostatic field along the chain were obtained within the finite field scheme, and the polarizability and second hyper-polarizability were compared with those extrapolated from oligomers. It was found that the polarizability and the second hyper-polarizability of trans polyacetylene are much larger than those obtained through quadratic extrapolation from oligomer polyenes, as shows the computational study starting from periodic boundary conditions is essentially important.