  Experiments conducted on two-dimensional twisted materials have revealed a
plethora of moir\'e patterns with different forms and shapes. The formation of
these patterns is usually attributed to the presence of small strains in the
samples, which typically arise during their fabrication. In this work we find
that the superlattice structure of such systems actually depends crucially on
the interplay between twist and strain. For systems composed of honeycomb
lattices, we show that this can lead to the formation of practically any
moir\'e geometry, even if each lattice is only slightly distorted. As a result,
we show that under strain the moir\'e Brillouin zone is not a stretched
irregular hexagon, but rather a primitive cell that changes according to the
geometry of the strained moir\'e vectors. We identify the conditions for the
formation of hexagonal moir\'e patterns arising solely due to shear or biaxial
strain, thus opening the possibility of engineering moir\'e patterns solely by
strain. Moreover, we study the electronic properties in such moir\'e patterns
and find that the strain tends to suppress the formation of the flat moir\'e
bands, even in the strain-induced hexagonal patterns analogous to those
obtained by the twist only. Our work explains the plethora of moir\'e patterns
observed in experiments, and provides a solid theoretical foundation from which
one can design moir\'e patterns by strain.
