Dirac and Weyl semimetals form an ideal platform for testing ideas developed in high energy physics to describe massless relativistic particles. One such quintessentially field-theoretic idea of chiral anomaly already resulted in the prediction and subsequent observation of the pronounced negative magnetoresistance in these novel materials for parallel electric and magnetic fields... Here we predict that the chiral anomaly occurs - and has experimentally observable consequences - when real electromagnetic fields E and B are replaced by strain-induced pseudo-electromagnetic fields e and b. For example, a uniform pseudomagnetic field b is generated when a Weyl semimetal nanowire is put under torsion. In accord with the chiral anomaly equation we predict a negative contribution to the wire resistance proportional to the square of the torsion strength. Remarkably, left and right moving chiral modes are then spatially segregated to the bulk and surface of the wire forming a "topological coaxial cable". This produces hydrodynamic flow with potentially very long relaxation time. Another effect we predict is the ultrasonic attenuation and electromagnetic emission due to a time periodic mechanical deformation causing pseudoelectric field e. These novel manifestations of the chiral anomaly are most striking in the semimetals with a single pair of Weyl nodes but also occur in Dirac semimetals such as Cd3As2 and Na3Bi and Weyl semimetals with unbroken time reversal symmetry. (read more)