Existing in vitro models of human skeletal muscle cannot recapitulate the organization and function of native muscle, limiting their use in physiological and pharmacological studies. Here, we demonstrate engineering of electrically and chemically responsive, contractile human muscle tissues ('myobundles') using primary myogenic cells. These biomimetic constructs exhibit aligned architecture, multinucleated and striated myofibers, and a Pax7+ cell pool. They contract spontaneously and respond to electrical stimuli with twitch and tetanic contractions. Positive correlation between contractile force and GCaMP6-reported calcium responses enables non-invasive tracking of myobundle function and drug response. During culture, myobundles maintain functional acetylcholine receptors and structurally and functionally mature, evidenced by increased myofiber diameter and improved calcium handling and contractile strength. In response to diversely acting drugs, myobundles undergo dose-dependent hypertrophy or toxic myopathy similar to clinical outcomes. Human myobundles provide an enabling platform for predictive drug and toxicology screening and development of novel therapeutics for muscle-related disorders.