In this paper we explore the conformational properties of random A-B block copolymers with semiflexible segments in a constant force field as a model of the behavior of biopolymers under tension. The degree of semiflexibility of individual blocks, which is characterized by a persistence length l, may range from values that correspond to complete flexibility of the block to values that correspond to nearly complete rigidity. The distribution of blocks is described by a two-state Markov process that generates the statistics governing the process of living polymerization in the steady state. Force-extension curves for this model of the polymer are calculated as an average over the chains conformations (which are described by a finitely extensible Gaussian model), as well as over both quenched and annealed distributions of the sequence of A and B blocks along the chain backbone. The results are sensitive to the nature of the sequence distribution: in the annealed case, the force-extension curves are sigmoidal for essentially all values of the parameters that characterize the conformational properties of the A and B blocks and their statistical correlations, while in the quenched case, the curves exhibit plateau regions that are reminiscent of various kinds of transitions in proteins and DNA. (C) 2003 American Institute of Physics.