It is more reasonable to adopt elliptical model to describe the attenuation of seismic intensity

but respective statistical analyses along major axis and minor axis may lead to inconsistent intensities of the attenuation relationships along two directions from the epicenter. In order to make the two attenuation relationships consistent

it requires us to resolve the difficulty of "limited head". At the same time

it is necessary to constrain the regression of the attenuation relationship of minor axis and thus make the calculated intensity always smaller than that from the attenuation relationship of major axis from the epicenter to the farther distance. This is the difficulty of "limited tail". Based on the above reasons and by using the method of regression with constraints

a constrained model of elliptical attenuation of seismic intensity is presented in this paper. The difficulty of limited head and tail on the curve of the attenuation relationship is resolved and the relationships between the magnitude and the radius to felt-area in regression are also taken into account. Based on the latest intensity data of North China that include 48 earthquakes and 139 isoseismal lines

the attenuation relationship of seismic intensity is obtained. A comparison between this result and other attenuation relationships of North China is made. It proved that our result is more reasonable at the long distance for large earthquake.