Abstract | Approximate methods based on the static pushover are introduced to estimate the seismic performance uncertainty of structures having non‐deterministic modeling parameters. At their basis lies the use of static pushover analysis to approximate Incremental Dynamic Analysis (IDA) and estimate the demand and capacity epistemic uncertainty. As a testbed we use a nine‐storey steel frame having beam hinges with uncertain moment–rotation relationships. Their properties are fully described by six, randomly distributed, parameters. Using Monte Carlo simulation with Latin hypercube sampling, a characteristic ensemble of structures is created. The Static Pushover to IDA (SPO2IDA) software is used to approximate the IDA capacity curve from the appropriately post‐processed results of the static pushover. The approximate IDAs allow the evaluation of the seismic demand and capacity for the full range of limit‐states, even close to global dynamic instability. Moment‐estimating techniques such as Rosenblueth’s point estimating method and the first‐order, second‐moment (FOSM) method are adopted as simple alternatives to obtain performance statistics with only a few simulations. The pushover is shown to be a tool that combined with SPO2IDA and moment‐estimating techniques can supply the uncertainty in the seismic performance of first‐mode‐dominated buildings for the full range of limit‐states, thus replacing semi‐empirical or code‐tabulated values (e.g. FEMA‐350), often adopted in performance‐based earthquake engineering.