  We present a toy model for the investigation of the formation of semilocal
strings, where a planar symmetry is employed to reduce the system to two
dimensions. We approximate the symmetry breaking using an extension of the
Vachaspati-Vilenkin algorithm, where we throw down random phases for the scalar
fields and then find the gauge field configuration which minimizes gradient
energy in this fixed scalar background. We show this procedure reproduces the
standard estimate for the formation rate of cosmic strings. For semilocal
strings the configurations generated by this method are ambiguous, and we
numerically evolve the configurations forward in time to identify which regions
form strings. We find a significant rate of formation, depending on the ratio
of couplings $\beta$. For low $\beta$ the formation rate is about one quarter
that of cosmic strings; this falls as $\beta$ is increased and above $\beta =
1$, where the string solution is dynamically unstable, no semilocal strings
form. We show the results are robust by examining different initial conditions
where, as expected in a thermal environment, the initial scalar field need not
be on the vacuum. We discuss implications for the three-dimensional case.
