Time series of production capital and total factor productivity (or "technology") are fundamental to understanding the processes of output and productivity growth. Unfortunately, capital and technology are unobserved except at the most disaggregated levels of production units and capital components and must be estimated prior to being used in empirical analysis. Standard methods for estimating capital and technology were developed decades ago and are based on analytical and computational methods of that era. We develop and apply a new method for estimating production capital and technology, based on advances in economics, dynamic optimization, statistics, and computing over the intervening years. The method involves specifying and estimating a detailed structural dynamic economic model of a representative production firm in an industry and using the estimated model to compute Kalman-smoothed estimates of unobserved capital and technology for the sample period. We apply the method to annual data from 1947-97 for U.S. total manufacturing industries and compare its capital and technology estimates with standard estimates reported by the Bureau of Labor Statistics..