Seed inputs are critical to the performance of mutation based fuzzers. Existing techniques make use of symbolic execution and gradient descent to generate seed inputs. However, these techniques are not particular suitable for input growth (i.e., making input longer and longer), a key step in seed input generation. Symbolic execution models very low level constraints and prefer fix-sized inputs whereas gradient descent only handles cases where path conditions are arithmetic functions of inputs. We observe that growing an input requires considering a number of relations: length, offset, and count, in which a field is the length of another field, the offset of another field, and the count of some pattern in another field, respective. Theory of string solver is particularly suitable for addressing these relations. We hence propose a novel technique called TensileFuzz, in which we identify input fields and denote them as string variables such that a seed input is the concatenation of these string variables. Additional padding string variables are inserted in between field variables. The aforementioned relations are reverse-engineered and lead to string constraints, solving which instantiates the padding variables and hence grows the input. Our technique also integrates linear regression and gradient descent to ensure the grown inputs satisfy path constraints that lead to path exploration. Our comparison with AFL, and a number of state-of-the-art fuzzers that have similar target applications, including Qsym, Angora, and SLF, shows that TensileFuzz substantially outperforms the others, by 39% - 98% in terms of path coverage.