We present a measurement of the elastic differential cross section $dsigma(pbar{p}rightarrow pbar{p})/dt$ as a function of the four-momentum-transfer squared t. The data sample corresponds to an integrated luminosity of $approx 31 nb^{-1}$ collected
with the D0 detector using dedicated Tevatron $pbar{p} $ Collider operating conditions at sqrt(s) = 1.96 TeV and covers the range $0.26 <|t|< 1.2 GeV^2$. For $|t|<0.6 GeV^2$, dsigma/dt is described by an exponential function of the form $Ae^{-b|t|}$ with a slope parameter $ b = 16.86 pm 0.10(stat) pm 0.20(syst) GeV^{-2}$. A change in slope is observed at $|t| approx 0.6 GeV^2$, followed by a more gradual |t| dependence with increasing values of |t|.
