Time-dependent solutions of the coupled Einstein-σ-model equations are studied analytically and numerically. We analyse in detail a spherically symmetric self-similar solution which describes the general relativistic collapse of a global texture. In view of the cosmological implications of the texture scenario for large scale structure formation, we derive exact analytical formulae for the light deflection, photon red shift and density fluctuations in the gravitational field of this texture solution. We also discuss the behavior of collisionless particles. Numerical results of a parameter study of other texture solutions are presented and are compared with the special self-similar solution.