The tensile strength of volcanic rocks is an important parameter for understanding and modelling a wide range of volcanic processes, and in the development of strategies designed to optimise energy production in volcanic geothermal reservoirs. However, despite the near-ubiquity of hydrothermal alteration at volcanic and geothermal systems, values of tensile strength for hydrothermally altered volcanic rocks are sparse. Here, we present an experimental study in which we measured the tensile strength of variably altered volcanic rocks. The alteration of these rocks, quantified as the weight percentage of secondary (alteration) minerals, varied from 6 to 62.8 wt%. Our data show that tensile strength decreases as a function of porosity, in agreement with previous studies, and as a function of alteration. We fit existing theoretical constitutive models to our data so that tensile strength can be estimated for a given porosity, and we provide a transformation of these models such that they are a function of alteration. However, because porosity and alteration influence each other, it is challenging to untangle their individual contributions to the measured reduction in tensile strength. Our new data and previously published data suggest that porosity exerts a first-order role on the tensile strength of volcanic rocks. Based on our data and observations, we also suggest that (1) alteration likely decreases tensile strength if associated with mineral dissolution, weak secondary minerals (such as clays), and an increase in microstructural heterogeneity and (2) alteration likely increases tensile strength if associated with pore- and crack-filling mineral precipitation. Therefore, we conclude that both alteration intensity and alteration type likely influence tensile strength. To highlight the implications of our findings, we provide discrete element method modelling which shows that, following the pressurisation of a dyke, the damage within weak hydrothermally altered host-rock is greater and more widespread than for strong hydrothermally altered host-rock. Because the rocks in volcanic and geothermal settings are likely to be altered, our results suggest that future modelling should consider the tensile strength of hydrothermally altered volcanic rocks.