WebAssembly (Wasm) is a safe, portable virtual instruction set that can be hosted in a wide range of environments, such as a Web browser. It is a low-level language whose instructions are intended to compile directly to bare hardware. While the initial version of Wasm focussed on single-threaded computation, a recent proposal extends it with low-level support for multiple threads and atomic instructions for synchronised access to shared memory. To support the correct compilation of concurrent programs, it is necessary to give a suitable specification of its memory model. Wasm’s language definition is based on a fully formalised specification that carefully avoids undefined behaviour. We present a substantial extension to this semantics, incorporating a relaxed memory model, along with a few proposed operational extensions. Wasm’s memory model is unique in that its linear address space can be dynamically grown during execution, while all accesses are bounds-checked. This leads to the novel problem of specifying how observations about the size of the memory can propagate between threads. We argue that, considering desirable compilation schemes, we cannot give a sequentially consistent semantics to memory growth. We show that our model guarantees Sequential Consistency of Data-Race-Free programs (SC-DRF). However, because Wasm is to run on the Web, we must also consider interoperability of its model with that of JavaScript. We show, by counter-example, that JavaScript’s memory model is not SC-DRF, in contrast to what is claimed in its specification. We propose two axiomatic conditions that should be added to the JavaScript model to correct this difference. We also describe a prototype SMT-based litmus tool which acts as an oracle for our axiomatic model, visualising its behaviours, including memory resizing.