Abstract The necessity of performing a detailed seismic fragility analysis of nuclear power plant components is well established in the nuclear industry. This paper focuses on the seismic fragility analysis of the primary containment structure of a typical Indian 700 MWe PHWR. The primary emphases of the fragility analysis adopted here are the detailed nonlinear modelling along with time-history analyses and the consideration of displacement-based failure limits. Three IDA-based methods and the conventional method using scaling/safety factors are used for fragility analysis and their results are compared. Among these, a new regression-based method proposed in this work provides better results than the existing methods. A modified version of this new method – for estimating fragilities for multiple limit states simultaneously – also provides similar results while reducing the level of statistical computation. The conventional method of fragility analysis fails to capture the (aleatory) randomness properly. In addition, compared to the peak ground acceleration, the fundamental mode spectral acceleration is found to have a better correlation with the damage measure for this structure, and is recommended for independent fragility analysis of such structures.