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We estimate with branching process models the propagation of load shed and the probability distribution of total load shed in simulated cascading blackouts of electric power systems. The average propagation of the simulated load shed data is estimated and then the initial load shed is propagated with two different branching process models of cascading failure to estimate the probability distribution of total load shed. The first model discretizes the load shed and then applies a Galton-Watson branching process. The second model is a continuous state branching process. We initially test the estimated distributions of total load shed using load shed data generated by the OPA and TRELSS cascading outage simulations. We discuss for the first model the effectiveness of the estimator in terms of how many cascades need to be simulated to predict the distribution of total load shed accurately.