Lifetime data with covariates (e.g., temperature, humidity, and electric current) are frequently seen in science and engineering. An important example is accelerated life testing (ALT) data. In ALT, test units of a product are exposing to severer-than-normal conditions to expedite product failure. The resulting lifetime and/or censoring data with covariates are often modeled by a probability distribution along with a life-stress relationship. However, if the probability distribution and the life-stress relationship selected cannot adequately describe the underlying failure process, the resulting reliability prediction will be misleading. This paper develops a new method for modeling lifetime data with covariates using phase-type (PH) distributions and a general life-stress relationship formulation. A numerical study is presented to compare the performance of this method with a mixture of Weibull distributions model. This general method creates a new direction for modeling and analyzing lifetime data with covariates for situations where the data-generating mechanisms are unknown or difficult to analyze using existing parametric ALT models and statistical tools.