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The thickness effect on electric breakdown strength (EBD) of four kinds of polymers under nanosecond pulses is investigated. The polymers are polyethylene, PTFE, PMMA, and nylon. The test samples are 0.5-3.5 mm in thickness (d) and are immersed in transformer oil. The nanosecond pulse is based on a Tesla-type generator, TPG200, which is with values of pulsewidth of 8.5 ns and rise time of 1.5 ns. The experimental results show that EBD is 1-2 MV/cm and decreases as d increases. The dependence of EBD on d is analyzed with the Weibull statistical distribution. It is concluded that logEBD versus log d is linear. By replotting the experimental data and by comparing with Martin's results, it is found that the slope for the linear dependence is about -1/8. With this conclusion, the breakdown probability is researched. It is shown that, to get a breakdown probability as low as 0.5%, the applied field should be decreased to about half of EBD.